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AN OPTIMAL CONTROL PROBLEM OF A FOOD CHAIN MODEL GOVERNED BY REACTION-DIFFUSION EQUATIONS 认领 引用
1
作者 Qixuan LIU Huili XIANG Min ZHOU 《Acta Mathematica Scientia》 SCIE CSCD 2026年第3期1463-1483,共21页
In this paper,a new nonlinear reaction-diffusion food chain model is proposed and an optimal control problem is established to maximize the total number of all populations in the model and minimize the total control c... In this paper,a new nonlinear reaction-diffusion food chain model is proposed and an optimal control problem is established to maximize the total number of all populations in the model and minimize the total control cost as much as possible.As the basis of theoretical analysis,the well-posedness and some estimates of the positive strong solution to the state system and the existence of the optimal pair are proven in a Hilbert space by employing the methods of functional analysis.Then,the first-order necessary optimality condition satisfied by the optimal control is obtained by using convex perturbation theory and duality techniques.Finally,a specific example and its numerical simulations are provided in order to confirm the theoretical results. 展开更多
关键词 reaction-diffusion food chain model the existence of the optimal control first order necessary optimality condition
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MARTINGALE SOLUTIONS OF FRACTIONAL STOCHASTIC REACTION-DIFFUSION EQUATIONS DRIVEN BY SUPERLINEAR NOISE 认领 引用
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作者 Bixiang WANG 《Acta Mathematica Scientia》 SCIE CSCD 2025年第6期2549-2578,共30页
In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Bot... In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Both the nonlinear drift and diffusion terms are not required to be locally Lipschitz continuous.We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-diffusion equation with polynomial drift driven by a superlinear noise.The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions defined by the Galerkin method. 展开更多
关键词 Martingale solution pseudo-monotonicity superlinear noise Skorokhod-Jakubowski theorem fractional equation stochastic reaction-diffusion equation
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MINIMUM WAVE SPEED OF A REACTION-DIFFUSION DENGUE MODEL WITH ASYMPTOMATIC CARRIER TRANSMISSION 认领 引用 被引量：1
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作者 Qin XING Rui XU 《Acta Mathematica Scientia》 SCIE CSCD 2025年第5期2088-2119,共32页
Dengue is a mosquito-borne disease that is rampant worldwide,with up to 70%of cases reported to be asymptomatic during epidemics.In this paper,a reaction-diffusion dengue model with asymptomatic carrier transmission i... Dengue is a mosquito-borne disease that is rampant worldwide,with up to 70%of cases reported to be asymptomatic during epidemics.In this paper,a reaction-diffusion dengue model with asymptomatic carrier transmission is investigated.We aim to study the existence,nonexistence and minimum wave speed of traveling wave solutions to the model.The results show that the existence and nonexistence of traveling wave solutions are fully determined by the threshold values,which are,the basic reproduction number R0 and critical wave speed c*>0.Specifically,when R0>1 and the wave speed c≥c*,the existence of the traveling wave solution is obtained by using Schauder's fixed point theorem and Lyapunov functional.It is proven that the model has no nontrivial traveling wave solutions for R0≤1 or R0>1 and 0<c<c*by employing comparison principle and limit theory.As a consequence,we conclude that the critical wave speed c*is the minimum wave speed of the model.Finally,numerical simulations are carried out to illustrate the effects of several important parameters on the minimum wave speed. 展开更多
关键词 dengue asymptomatic carriers reaction-diffusion traveling wave solutions minimum wave speed
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Turing instability-induced oscillations in coupled reaction-diffusion systems 认领 引用
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作者 Nan Wang Yuan Tong +3 位作者 Fucheng Liu Xiaoxuan Li Yafeng He Weili Fan 《Chinese Physics B》 SCIE EI CAS CSCD 2025年第3期541-548,共8页
A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary ... A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained.A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns.Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally,undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations.It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns.When the size is large,localized traveling waves such as spirals and targets emerge.These results may be useful for deeper understanding of pattern formation in complex systems,particularly multilayered systems. 展开更多
关键词 oscillations localized oscillatory pattern Turing instability coupled reaction-diffusion system
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EXPONENTIAL STABILITY OF ATTRACTOR FOR RANDOM REACTION-DIFFUSION EQUATION DRIVEN BY NONLINEAR COLORED NOISE ON RN 认领 引用
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作者 Huijuan ZHU Xiaojun LI Yanjiao LI 《Acta Mathematica Scientia》 SCIE CSCD 2025年第4期1567-1596,共30页
In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onRN . The key steps of the proof ar... In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onRN . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on RN . 展开更多
关键词 random reaction-diffusion equation continuous cocycle pullback random attractor fractal dimension random exponential attractor
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Weak Mean Attractor of Stochastic Reaction-Diffusion Equation with Superlinear Multiplicative Noise and Strong Dissipativity Supercritical Nonlinearities 认领 引用
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作者 QI Ailing JU Xuewei TONG Xiaoting 《数学理论与应用》 2025年第4期28-49,共22页
This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate ... This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate β,is strongly dissipative and the diffusion term σ(u)has growth rate γ,satisfying β+1>2γ.Under this condition,we establish the existence,uniqueness,and regularity of solutions in Bochner spaces.Our analysis relies only on weak monotonicity conditions and requires no further growth restrictions on f andσ.Moreover,we prove the existence of a weak mean random attractor for the system.These results offer new insights into the balance mechanism between stochastic perturbations and dissipative effects in superlinear regimes. 展开更多
关键词 Stochastic reaction-diffusion equation Strongly dissipative drift term Superlinear noise Bochner space Weak mean attractor
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High accuracy non-equidistant method for singular perturbation reaction-diffusion problem 认领 引用 被引量：5
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作者 蔡新 蔡丹琳 +1 位作者 吴瑞潜 谢康和 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第2期175-182,共8页
Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region.... Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result. 展开更多
关键词 singular perturbation reaction-diffusion uniform convergence high accuracy non-equidistant
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Symmetry Analysis and Conservation Laws to the(2+1)-Dimensional Coupled Nonlinear Extension of the Reaction-Diffusion Equation 认领 引用 被引量：5
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作者 陈俊超 辛祥鹏 陈勇 《Communications in Theoretical Physics》 SCIE CAS CSCD 2014年第8期173-182,共10页
In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple dire... In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem. 展开更多
关键词 (2+1)-dimensional coupled nonlinear reaction-diffusion equation Lie symmetry invariant solutions optimal system conservation laws
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Concentration fluctuation caused by reaction-diffusion coupling near catalytic active sites 认领 引用 被引量：2
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作者 Haolei Zhang Mingcan Zhao +2 位作者 Yanping Li Chengxiang Li Wei Ge 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2022年第10期254-263,共10页
The coupling of reaction and diffusion between neighboring active sites in the catalyst pore leads to the spatiotemporal fluctuation in component concentration,which is very importa nt to catalyst performance and henc... The coupling of reaction and diffusion between neighboring active sites in the catalyst pore leads to the spatiotemporal fluctuation in component concentration,which is very importa nt to catalyst performance and hence its optimal design.Molecular dynamics simulation with hard-sphere and pseudo-particle modeling has previously revealed the non-stochastic concentration fluctuation of the reactant/product near isolated active site due to such coupling,using a simple model reaction of A→B in 2D pores.The topic is further developed in this work by studying the concentration fluctuation due to such coupling between neighboring active sites in 3D pores.Two 3D pore models containing an isolated active site and two adjacent active sites were constructed,respectively.For the isolated site,the concentration fluctuation intensifies for larger pores,but the product yield decreases,and for a given pore size,the product yield reaches a peak at a certain reactant concentration.For two neighboring sites,their distance(d)is found to have little effect on the reaction,but significant to the diffusion.For the same reaction competing at both sites,larger d leads to more efficient diffusion and better overall performance.However,for sequential reactions at the two sites,higher overall performance presents at a smaller d.The results should be helpful to the catalyst design and reaction control in the relevant processes. 展开更多
关键词 Molecular dynamicssimulation Concentration fluctuation Reaction-diffusion coupling Catalyst
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GLOBAL STABILITY OF TRAVELING WAVEFRONTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY 认领 引用 被引量：5
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作者 杨兆星 张国宝 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期289-302,共14页
This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability o... This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts （waves with speeds c 〉 c＊, where c=c＊ is the minimal speed） is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21]. 展开更多
关键词 nonlocal reaction-diffusion equations traveling wavefronts stability compari- son principle weighted energy method
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ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS 认领 引用 被引量：3
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作者 韩豪 张诚坚 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1865-1880,共16页
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their... This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results. 展开更多
关键词 neutral reaction-diffusion equations piecewise continuous arguments asymptotical stability finite element methods numerical experiment
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STOCHASTIC CRACKING AND HEALING BEHAVIORS OF THIN FILMS DURING REACTION-DIFFUSION GROWTH 认领 引用 被引量：8
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作者 S.L. Zhu, S.L. Yang, Y.M. Xiong, M.S. Li, S.J. Geng, C.S. Hu, Fuhui Wang and W.T. Wu 《Acta Metallurgica Sinica(English Letters)》 EI CAS 2001年第6期544-548,共5页
The stochastic cracking and healing behaviors of reaction-diffusion growth of thin filmswere studied by means of Markov processes analysis. We chose the thermal growth ofoxide scales on metals as an example of reactio... The stochastic cracking and healing behaviors of reaction-diffusion growth of thin filmswere studied by means of Markov processes analysis. We chose the thermal growth ofoxide scales on metals as an example of reaction-diffusion growth. The thermal growthof oxide films follows power law when no cracking occurs. Our results showed that thegrowth kinetics under stochastic cracking and healing conditions was different fromthat without cracking. It might be altered to either pseudo-linear or pseudo-power lawsdependent upon the intensity and frequency of the cracking of the films. When thehoping items dominated, the growth followed pseudo-linear law; when the diffusionalitems dominated, it followed pseudo-power law with the exponentials lower than theintrinsical values. The numerical results were in good agreement with the meassuredkinetics of isothermal and cyclic oxidation of NiAl-0.1 Y (at. %) alloys in air at 1273K. 展开更多
关键词 stochastic analysis reaction-diffusion growth oxide films
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Finite volume element method for analysis of unsteady reaction-diffusion problems 认领 引用 被引量：1
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作者 Sutthisak Phongthanapanich Pramote Dechaumphai 《Acta Mechanica Sinica》 SCIE EI CAS 2009年第4期481-489,共9页
A finite volume element method is developed for analyzing unsteady scalar reaction-diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element m... A finite volume element method is developed for analyzing unsteady scalar reaction-diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction-diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the high-gradient boundary layers. 展开更多
关键词 Finite volume element method Explicitmethod Unsteady problem Singularly perturbed equation Reaction-diffusion
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Exact Solutions and Invariant Sets to General Reaction-Diffusion Equation 认领 引用 被引量：1
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作者 JIA Hua-Bing XU Wei 《Communications in Theoretical Physics》 SCIE CAS 2008年第6期1389-1392,共4页
In this paper,we introduce new invariant sets,and the invariant sets and exact solutions to general reactiondiffusion equation are discussed.It is shown that there exist a class of exact solutions to the equations tha... In this paper,we introduce new invariant sets,and the invariant sets and exact solutions to general reactiondiffusion equation are discussed.It is shown that there exist a class of exact solutions to the equations that belong to the invariant sets. 展开更多
关键词 invariant set exact solution general reaction-diffusion equation rotation group scaling group
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UNIFORM QUASI-DIFFERENTIABILITY OF SEMIGROUP TO NONLINEAR REACTION-DIFFUSION EQUATIONS WITH SUPERCRITI C AL EXPONENT 认领 引用 被引量：1
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作者 钟延生 孙春友 《Acta Mathematica Scientia》 SCIE CSCD 2017年第2期301-315,共15页
A new approach, is established to show that the semigroup {S（t）≥0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in L^q（Ω） （2 ≤ q 〈 ∞） with respect ... A new approach, is established to show that the semigroup {S（t）≥0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in L^q（Ω） （2 ≤ q 〈 ∞） with respect to the initial value. As an application, this proves the upper-bound of fractal dimension for its global attractor in the corresponding space. 展开更多
关键词 Uniform quasi-differentiability semigroup reaction-diffusion equation
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The First Integral Method to Study a Class of Reaction-Diffusion Equations 认领 引用 被引量：1
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作者 KEYun-Quant YUJun 《Communications in Theoretical Physics》 SCIE CAS 2005年第4期597-600,共4页
In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by usi... In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method. 展开更多
关键词 exact solution reaction-diffusion equation first integral
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Numerical Simulation of Reaction-Diffusion during Carburization of HK40 Steel 认领 引用 被引量：3
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作者 Meili ZHU, Qiang XU and Junshan ZHANGDepartment of Materials Engineering, Dalian University of Technology, Dalian 116024, China 《Journal of Materials Science & Technology》 SCIE EI CAS 2003年第4期327-330,共4页
Two types of carbides M23C6 and M7C3 precipitate orderly as carbon concentration in a high Cr-Ni austenitic steel increases during carburization process. The mathematical model that describes diffusion of carbon and t... Two types of carbides M23C6 and M7C3 precipitate orderly as carbon concentration in a high Cr-Ni austenitic steel increases during carburization process. The mathematical model that describes diffusion of carbon and the precipitation of M23C6 and M7C3 has been studied. A criterion to judge when the transformation of M23C6 to M7C3 is over and M7C3 precipitates directly has been given in simulated calculation. By applying the model, the carburization of HK40 steel has been calculated by means of finite difference computation techniques. The pack carburization tests for the HK40 steel have been carried out at 1273 K. The comparison between the experimental and the calculated results show acceptable agreement. 展开更多
关键词 Reaction-diffusion HK40 steel Carburization
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Improving the Stability Problem of the Finite Difference Scheme for Reaction-diffusion Equation 认领 引用 被引量：2
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作者 XU Chen-mei 《Chinese Quarterly Journal of Mathematics》 北大核心 2008年第3期403-408,共6页
This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incr... This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme. 展开更多
关键词 reaction-diffusion equation difference scheme stability problem incremental unknowns
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THE EXTINCTION BEHAVIOR OF THE SOLUTIONS FOR A CLASS OF REACTION-DIFFUSION EQUATIONS 认领 引用 被引量：1
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作者 CHEN Song-lin 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第11期1352-1356,共5页
The methods of L-p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boundary values partial derivativeu/partial derivativet = Deltau -... The methods of L-p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boundary values partial derivativeu/partial derivativet = Deltau - lambda \u\(gamma-1) u - betau ((x, t) is an element of Omega x (0, + infinity)), u(x, t) \(partial derivativeOmegax (0, +infinity)) = 0, u(x, 0) = u(0) (x) is an element of H-0(1) (Omega) boolean AND L1+gamma(Omega) (x is an element of Omega). Sufficient and necessary conditions about the extinction of the solutions is given. Here lambda > 0, gamma > 0, beta > 0 are constants, Omega is an element of R-N is bounded with smooth boundary partial derivativeOmega. At last, it is simulated with a higher order equation by using the present methods. 展开更多
关键词 reaction-diffusion equation extinction L-p estimation Bernoulli equation
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Asymptotic solution of nonlocal nonlinear reaction-diffusion Robin problems with two parameters 认领 引用 被引量：1
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作者 莫嘉琪 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第8期1003-1008,共6页
In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed ... In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed in relation to two small parameters. The asymptotic solutions of the problem are given. 展开更多
关键词 problem reaction-diffusion system singular perturbation initial boundary value
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