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SOME NEW REGULARITY CRITERIA OF THE INCOMPRESSIBLE 3D MHD EQUATIONS 认领 引用
1
作者 Honglin ZHANG Li LI Qingning ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2026年第3期1340-1357,共18页
In this paper,we investigate several regularity criteria to the 3D incompressible magnetohydrodynamic equations.These criteria are based on certain assumptions made in partial elements of the velocity gradient tensor ... In this paper,we investigate several regularity criteria to the 3D incompressible magnetohydrodynamic equations.These criteria are based on certain assumptions made in partial elements of the velocity gradient tensor and pressure,respectively.By making use of the Littlewood-Paley decomposition,we show that the solution(u,b)can be smoothly extended after time T if any two groups of functions(∂1u1,∂1b1),(∂2u2,∂2b2)and(∂3u3,∂3b3belong to the space L1(0,T;B∞,∞). 展开更多
关键词 magnetohydrodynamic equations Navier-Stokes equations regularity criteria Besov space Littlewood-Paley decomposition
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Multi-antiderivative transformation alternating iterative deep learning method for solving anisotropic scattering neutron transport equations 认领 引用
2
作者 Dong Liu Bin Zhang +4 位作者 Qi Luo Heng Zhang Yong Jiang Xian-Tao Cui Chen Zhao 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2026年第5期375-393,共19页
Deep learning methods have achieved significant progress in solving partial differential equations.However,when applied to the widely used anisotropic scattering neutron transport equations in reactor engineering,thes... Deep learning methods have achieved significant progress in solving partial differential equations.However,when applied to the widely used anisotropic scattering neutron transport equations in reactor engineering,these encounter significant challenges.To address this issue,this study introduces a multi-antiderivative transformation alternating iterative deep learning method(M-AIM).This method transforms the integral terms of the scattering and fission sources in the transport equation into multiple antiderivative functions corresponding to the integrand,converts the differential-integral form of the transport equation into an exact differential equation,and establishes the necessary constraints for a unique solution.The M-AIM uses multiple deep neural networks to map the unknown angular flux density of transport equations and represents various forms of antiderivative functions.It constructs the corresponding weighted loss functions.By alternating iterative training with deep learning methods applied to these neural networks,the loss is reduced gradually.When the loss decreases to a preset minimum,the neural network approaches a numerical solution for both angular flux density and antiderivative functions.This paper presents a numerical verification of geometries such as flat plates and spheres.It verifies the validity of the theoretical framework and associated methods.The study contributes to the development of novel technical approaches for applying deep learning to solve anisotropic scattering neutron transport equations in reactor engineering. 展开更多
关键词 Neutron transport equations Anisotropic scattering Multi-antiderivative Alternating iteration Deep learning
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Numerical method for solving dynamical equations of multibody systems with nonholonomic constraints based on state-space method 认领 引用
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作者 Jiajun Wu Xian Guo +3 位作者 Dingguo Zhang Yue Zhang Liang Li Kang Guo 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第7期505-520,共16页
In this paper,a new numerical solution method is proposed for dealing with differential-algebraic equations(DAEs)for dynamics of multibody systems with nonholonomic constraints.The nonholonomic constraints directly re... In this paper,a new numerical solution method is proposed for dealing with differential-algebraic equations(DAEs)for dynamics of multibody systems with nonholonomic constraints.The nonholonomic constraints directly restrict the velocity coor-dinates,resulting in no corresponding position constraint equations.Therefore,the traditional state-space method is insufficient to solve such DAEs.In the proposed state-space method,direct integration of the ordinary differential equations obtained from the index-1 DAEs,ensures that the acceleration constraints are satisfied and provides initial values for the dependent variables.Subsequently,position and velocity constraint equations are solved to update dependent variables,strictly ensuring satisfaction of constraints at three levels.Currently,LU decomposition is the most used method to define the state-space method.However,in order to ensure the accuracy and stability of the algorithm,coordinate identification is required at every time step,which reduces the computational efficiency.Therefore,in this paper,the state-space method defined by singular value decomposition(SVD)is proposed,which does not require frequent coordinate identification and improves the computational efficiency.Numerical exam-ples show that the state-space method based on SVD outperforms the LU decomposition in terms of computational efficiency and stability. 展开更多
关键词 Multibody system dynamics Nonholonomic constraints Differential algebraic equations State-space method
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Fitting equations for the sorption isotherms of cement mortar with salt spray deposition 认领 引用
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作者 Bing Li Roberto Giordano +3 位作者 Jean-Marc Tulliani Saierjiang Halike Wanjiang Wang Qinglin Meng 《Frontiers of Architectural Research》 EI CSCD 2026年第3期845-857,共13页
The sorption isotherm of porous building materials serves as a critical hygrothermal property that regulates coupled heat and moisture transfer and influences the energy effi-ciency of building envelopes.Coastal build... The sorption isotherm of porous building materials serves as a critical hygrothermal property that regulates coupled heat and moisture transfer and influences the energy effi-ciency of building envelopes.Coastal buildings endure chronic salt spray exposure,yet clas-sical fitting equations neglect salt deposition effects.This study investigates cement mortar specimens subjected to accelerated salt spray tests(0—35 cycles).The salt content of the specimens was quantified via chloride ion analysis,and isothermal sorption tests were con-ducted under 33%—93%relative humidity(RH)using a static equilibrium method.A modified model integrating a salt influence factor(ηu)into classical equations was developed.Addition-ally,dual-regime sorption isotherm models were formulated based on deliquescence mecha-nisms of salt crystals above critical humidity,governed by the Robinson equation and Nielsen model,respectively.This framework enables accurate prediction of equilibrium mois-ture content under varying coupled humidity-salt conditions,significantly enhancing the reli-ability of hygrothermal simulations for coastal buildings in salt spray climates. 展开更多
关键词 Salt spray climate Cement mortar Sorption isotherm Fitting equations
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Blow-up results for the weakly coupled system of semilinear wave equations with weak dampings 认领 引用
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作者 MING Sen FAN Xiong-mei +1 位作者 REN Cui XIE Jin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2026年第1期1-20,共20页
This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions(namely,the Dirichlet,Neumann,and Robin boundary cond... This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions(namely,the Dirichlet,Neumann,and Robin boundary conditions).Blow-up results and lifespan estimates of solutions to the problem with two different types of weak damping terms and power nonlinearities in the sub-critical and critical cases on exterior domain are obtained.The test function technique is performed in the proofs.It is worth observing that our results in Theorem 1.1 in this article contain the results in[6]as a special case whenθ=0.To the best of our knowledge,the results in Theorems 1.1-1.2 are new. 展开更多
关键词 initial boundary value problem semilinear wave equations weak damping terms lifespan estimates test function technique
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ANALYSIS OF A QUADRILATERAL EDGE ELEMENT METHOD FOR MAXWELL EQUATIONS 认领 引用
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作者 Zhijie DU Huoyuan DUAN Caihong WANG 《Acta Mathematica Scientia》 SCIE CSCD 2026年第1期275-292,共18页
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob... A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition). 展开更多
关键词 Maxwell equations finite element method quadrilateral mesh stability error bound spectral approximation
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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR INITIAL-BOUNDARY VALUE PROBLEMS OF ONE-DIMENSION QUASILINEAR WAVE EQUATIONS WITH NULL CONDITIONS 认领 引用
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作者 Dongbing ZHA Yitong SUN Tingqiang HOU 《Acta Mathematica Scientia》 SCIE CSCD 2026年第2期568-594,共27页
We consider the initial-boundary value problems on R+×R+ for one-dimension systems of quasilinear wave equations with null conditions.We first show that for homogeneous Dirichlet boundary values and suffici... We consider the initial-boundary value problems on R+×R+ for one-dimension systems of quasilinear wave equations with null conditions.We first show that for homogeneous Dirichlet boundary values and sufficiently small initial data,classical solutions always globally exist.Then we prove that the global solution will scatter,i.e.,it will converge to some solution of one dimensional homogeneous linear wave equations as time tends to infinity,in the energy sense.Finally we show the inverse scattering result:the scattering data can determine the global solution uniquely. 展开更多
关键词 one-dimension quasilinear wave equations null condition global existence scattering inverse scattering
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On the Global Well-Posedness of 2D tα-Type Boussinesq Equations 认领 引用
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作者 Fang WANG Fengqun TANG +1 位作者 Yao TAN Yanling LI 《Journal of Mathematical Research with Applications》 CSCD 2026年第3期364-388,共25页
We study a special type of Boussinesq equations{δtu+u・∇u+∇P=νtα△u+θe2,δt+u・∇θ=κ△θ,∇・u=0with time-dependent viscosity coefficients,termed as tα-type Boussinesq equations.By skillfully combinin... We study a special type of Boussinesq equations{δtu+u・∇u+∇P=νtα△u+θe2,δt+u・∇θ=κ△θ,∇・u=0with time-dependent viscosity coefficients,termed as tα-type Boussinesq equations.By skillfully combining Schauder's fixed-point theorem with integrating factor techniques under the parameter constraint 0<α<1,we establish the existence and uniqueness of classical solutions for H3initial data.The analytical framework developed in this work provides a self-contained methodology with independent theoretical value. 展开更多
关键词 Boussinesq equations Schauder fixed-point theorem integrating factor method
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ANALYSIS ON EXACT SOLUTIONS FOR THE INCOMPRESSIBLE EULER EQUATIONS IN RN 认领 引用
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作者 Xinglong WU Boling GUO 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1827-1840,共14页
The present is concerned with the study of blow-up and global existence of the spherically symmetric solutions for the incompressible Euler equations in RN for any dimension N≥2.The approach is to construct explicit ... The present is concerned with the study of blow-up and global existence of the spherically symmetric solutions for the incompressible Euler equations in RN for any dimension N≥2.The approach is to construct explicit solution with spherical symmetry to study certain blow-up and no blow-up phenomena of solutions to the incompressible Euler equation in RN. 展开更多
关键词 the incompressible Euler equations blow-up phenomena global existence of solution spherically symmetric solutions the asymptotic behavior
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EXISTENCE OF NORMALIZED SOLUTIONS TO LAPLACIAN-LIKE EQUATIONS AT SUBCRITICAL GROWTH 认领 引用
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作者 Zhouxin LI Yuan XIANG 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1841-1861,共21页
In this paper,we study a class of Laplacian-like equation.We first deduce the Pohozaev identity of the equation and consider the minimum of the functional on the Pohozaev manifold and then study the properties of the ... In this paper,we study a class of Laplacian-like equation.We first deduce the Pohozaev identity of the equation and consider the minimum of the functional on the Pohozaev manifold and then study the properties of the minimum energy of the functional.Based on the properties obtained,we prove the existence of normalized solution to the equation. 展开更多
关键词 normalized solutions Laplacian-like equations Pohozaev identity
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Solvability of bipolar max-product fuzzy relation equations and inequalities with product negation 认领 引用
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作者 Hongpeng Li Haitao Li 《Control Theory and Technology》 EI CSCD 2026年第3期504-513,共10页
Bipolar max-product fuzzy relation equations(BMPFREs)with product negation are important in decision-making because of the consideration of both positive and negative effects.In this paper,the solvability of BMPFREs w... Bipolar max-product fuzzy relation equations(BMPFREs)with product negation are important in decision-making because of the consideration of both positive and negative effects.In this paper,the solvability of BMPFREs with product negation whose independent terms may take the value zero is considered.Based on the matrix representation of BMPFREs with product negation,a bipolar constraint matrix is constructed.A new necessary and sufficiency condition is proposed by exploring the structural features of bipolar constraint matrix,and all solutions are derived to solve BMPFREs.As an application of the bipolar constraint matrix method,the solvability of a special kind of bipolar max-product fuzzy relation inequalities(BMPFRIs)with product negation is further discussed. 展开更多
关键词 Bipolar fuzzy relation equations Max-product composition Product negation Bipolar constraint matrix
CHARACTERISTICS OF ROGUE WAVES IN THE SCALAR AND VECTOR NONLOCAL NONLINEAR SCHRÖDINGER EQUATIONS 认领 引用
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作者 Xiu-Bin WANG Shou-Fu TIAN 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1794-1808,共15页
In this work,the theoretical calculation of general higher-order rogue wave solutions for parity-time symmetric scalar and vector nonlocal nonlinear Schrödinger equations is conducted via a DDT using a separation... In this work,the theoretical calculation of general higher-order rogue wave solutions for parity-time symmetric scalar and vector nonlocal nonlinear Schrödinger equations is conducted via a DDT using a separation of the variable technique.Furthermore,to gain a deeper comprehension of our findings,the main characteristics of the obtained solutions are displayed graphically.Our findings indicate that the dynamics of these solutions exhibit a rich array of patterns,most of which have no counterparts in the corresponding local equations. 展开更多
关键词 the scalar and vector nonlocal nonlinear Schrödinger equations rogue waves Darboux-dressing transformation(DDT) a variable separation technique
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Informed Reconstruction-Oriented Numerical Networks:A More Efficient Method for Solving Multiple Unknown Parameters of Manakov Equations 认领 引用
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作者 Peng-Fei Wang Yun-Zhou Sun +1 位作者 Houria Triki Qin Zhou 《Chinese Physics Letters》 SCIE EI CAS CSCD 2026年第4期21-28,共8页
By simultaneously introducing a finite-difference-based numerical loss term and a clustering-reconstruction mechanism,we propose an enhanced physics-informed neural network named the informed reconstruction-oriented n... By simultaneously introducing a finite-difference-based numerical loss term and a clustering-reconstruction mechanism,we propose an enhanced physics-informed neural network named the informed reconstruction-oriented numerical network(IRON-Net)and subsequently apply it to the Manakov equations-a well-known two-component nonlinear physical model.Numerical experiments are conducted on a dataset containing eight analytical solu-tions with noise.The results indicate that,compared to conventional PINNs and other mainstream algorithms,IRON-Net demonstrates significant advantages in training accuracy,convergence rate,and robustness,achiev-ing a stepwise improvement in the neural network’s ability to enforce physical constraints.Additional ablation experiments further confirm the necessity of the consistency constraint within IRON-Net.This study provides an effective approach for modeling and parameter identification in complex nonlinear optical systems as well as other nonlinear physical scenarios. 展开更多
关键词 clustering reconstruction mechanism training accuracy analytical solu tions conventional pinns informed reconstruction oriented numerical networks finite difference based numerical loss term physics informed neural network manakov equations
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STABILITY OF PLANAR RAREFACTION WAVE TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE 认领 引用
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作者 Nangao ZHANG Xuan MA 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1751-1772,共22页
In this paper,we are concerned with the large-time behavior of solution to the Cauchy problem for the 3D compressible Navier-Stokes equations for a reacting mixture in an infinite long flat nozzle domain R×T2.... In this paper,we are concerned with the large-time behavior of solution to the Cauchy problem for the 3D compressible Navier-Stokes equations for a reacting mixture in an infinite long flat nozzle domain R×T2.Under some smallness conditions on the initial perturbations,we prove that the solution to this system exists globally and tends timeasymptotically to the planar rarefaction wave,in which the background solutionz(x,t)of the mass fraction of the reactant is nontrivial.The proof is accomplished by virtue of delicate energy method.To the best of our knowledge,this may be the first result about the nonlinear stability of the plane waves for the compressible Navier-Stokes equation for a reacting mixture. 展开更多
关键词 Navier-Stokes equations planar rarefaction wave energy method
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Ulam-Hyers stability of nonlinear integro-differential equations having complex fractional order 认领 引用
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作者 Pratibha Verma Surabhi Tiwari 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2026年第2期455-479,共25页
This article discusses the two-step Adomian decomposition method for solving nonlinear integro-differential equations of complex fractional order to obtain an analytical solution using a simple algorithm.We obtain the... This article discusses the two-step Adomian decomposition method for solving nonlinear integro-differential equations of complex fractional order to obtain an analytical solution using a simple algorithm.We obtain the analytical solution using only one iteration.We find the results without using the approximation and discretization tools,which generally generate the round-off error.The obtained solution has higher accuracy than other numerical methods.We consider two examples to prove the applicability of the method and compare the results with other numerical methods.Here,we use the Caputo definition for complex fractional order operators.We provide new results such as the existence,uniqueness,and stability of the solution of the complex fractional nonlinear integro-differential equations(CF-NL-IDEs)employing the fixed point theory and Ulam-Hyers stability.Additionally,we solve examples using two popular numerical methods:the Adomian decomposition method and the modified Adomian decomposition method.We also compare the solution obtained from the proposed method and the solutions obtained from these two numerical methods.It is observed via examples that our method provides more accurate results with faster convergence for the CF-NL-IDEs. 展开更多
关键词 integro-differential equations Caputo complex fractional derivative two-step Adomian decomposition method fixed point theory Ulam-Hyers stability
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Residual resampling-based physics-informed neural network for neutron diffusion equations 认领 引用
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作者 Heng Zhang Yun-Ling He +3 位作者 Dong Liu Qin Hang He-Min Yao Di Xiang 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2026年第2期16-41,共26页
The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN app... The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN approaches generally utilize a fully connected network(FCN)architecture that is susceptible to overfitting,training instability,and gradient vanishing as the network depth increases.These challenges result in accuracy bottlenecks in the solution.In response to these issues,the residual-based resample physics-informed neural network(R2-PINN)is proposed.It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut(S-CNN).It incorporates skip connections to facilitate gradient propagation between network layers.Additionally,the incorporation of the residual adaptive resampling(RAR)mechanism dynamically increases the number of sampling points.This,in turn,enhances the spatial representation capabilities and overall predictive accuracy of the model.The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields.Compared with conventional FCN-based PINN methods,R 2-PINN effectively overcomes the limitations inherent in current methods.Thus,it provides more accurate and robust solutions for neutron diffusion equations. 展开更多
关键词 Neutron diffusion equation Physics-informed neural network CNN with shortcut Residual adaptive resampling
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Moment flux-based discrete velocity method based on the Boltzmann-BGK equations along the characteristic line 认领 引用
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作者 Wei Liu Yong Liu Haihu Liu 《Theoretical & Applied Mechanics Letters》 EI CAS CSCD 2026年第3期110-120,共11页
This paper introduces an improved scheme based on the discrete velocity method.Specifically,the reconstruction of the velocity distribution function and numerical flux at the interface is founded on the solution of th... This paper introduces an improved scheme based on the discrete velocity method.Specifically,the reconstruction of the velocity distribution function and numerical flux at the interface is founded on the solution of the Bhatnagar-Gross-Krook equation along the characteristic line.The proposed method accurately considers molecular transport and collision effects at the interface,thereby enabling accurate modeling from rarefied to continuum flow regimes.Additionally,the implicit discretization of the microscopic equations and incorporation of macroscopic equations result in accelerated convergence properties for steady-state problems.The proposed numerical approach is validated through several cases,including Rayleigh flow,lid-driven cavity flow,flow past an NACA0012 airfoil,and supersonic flow around a sphere.Numerical results demonstrate that the proposed method can efficiently and accurately obtain multiscale flow properties. 展开更多
关键词 Rarefied flow Boltzmann equation Moment method Finite volume method
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A Bessel-Class Radial Basis Function for Neural Networks in Solving Helmholtz and Laplace Equations 认领 引用
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作者 Quan Jiang Shexu Zhao 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2026年第6期766-781,共16页
Helmholtz and Laplace equations are important in mechanics.A Bessel-class radial basis functions(RBFs)is introduced in neural networks to solve Laplace and Helmholtz equations.This class of RBFs is proved to be contin... Helmholtz and Laplace equations are important in mechanics.A Bessel-class radial basis functions(RBFs)is introduced in neural networks to solve Laplace and Helmholtz equations.This class of RBFs is proved to be continuous and infinite positive definite.The presented Bessel-class RBF can degenerate to Gaussian in an infinite smooth case.The presented RBF satisfies Helmholtz equations in the domain,and does not need physics regularization.It can also be applied to Laplace equation by applying a small artificial parameter.Thus,the presented RBF can be used in RBF neural networks to solve Helmholtz and Laplace equations only by training data on the boundary.Several numerical examples including Helmholtz and Laplace equations have been carried out to show the effectiveness of this Bessel-class RBFs in 1-D,2-D and 3-D domain,respectively. 展开更多
关键词 Machine learning RBF neural network Bessel-class activation function Laplace equation Helmholtz
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Global Well-Posedness for 3D Generalized MHD-Boussinesq Equations 认领 引用
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作者 Xiao LI Qiuyue ZHANG 《Journal of Mathematical Research with Applications》 CSCD 2026年第2期235-250,共16页
We investigate the three-dimensional(3D)generalized magnetohydrodynamic(MHD)-Boussinesq system with fractional dissipation and damping terms,aiming to establish the well-posedness theory for the 3D incompressible temp... We investigate the three-dimensional(3D)generalized magnetohydrodynamic(MHD)-Boussinesq system with fractional dissipation and damping terms,aiming to establish the well-posedness theory for the 3D incompressible temperature-dependent MHD-Boussinesq equations with damping.By exploiting the structural properties of the system and performing refined a priori estimates,we address the global well-posedness of solutions under the weakest possible dissipation conditions. 展开更多
关键词 MHD-Boussinesq equation Global well-posedness damping
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On Petrenko's Deviations and Complex Difference Equations 认领 引用
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作者 Lipeng XIAO Chunfang CHEN 《Journal of Mathematical Research with Applications》 CSCD 2026年第2期209-221,共13页
In this paper,the growth characteristic of meromorphic solutions for the following difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0 with no dominating coefficient is studied.By imposing certain restriction o... In this paper,the growth characteristic of meromorphic solutions for the following difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0 with no dominating coefficient is studied.By imposing certain restriction on the entire coefficients associated with Petrenko's deviation of the above equation,we obtain some results and partially address a question posed byⅠ.Laine and C.C.Yang.Furthermore,for the entire solutions f(z)of the difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=F(z),where Aj(z)(j=0,…,n),F(z)are entire functions,we discover a close relationship between the measure of common transcendental directions associated with classical difference operators of f(z)and Petrenko's deviations of the coefficients. 展开更多
关键词 complex difference equation difference operator Petrenko’s deviation transcenden-tal direction
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