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THE SECOND INITIAL-BOUNDARY VALUE PROBLEM FOR A QUASILINEAR PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS 认领 引用
1
作者 潘佳庆 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第11期1331-1337,共7页
With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are in... With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigated. The main results are : 1) there exists only one global weak solution which continuously depends on initial value; 2) when t < T-0, the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough. 展开更多
关键词 fast-diffusion quasilinear nonlinear boundary conditions second initial-boundary value problem
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EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM 认领 引用 被引量：3
2
作者 戴正德 蒋慕蓉 《Acta Mathematica Scientia》 SCIE 2000年第4期451-460,共10页
The equation of pattern formation induced by buoyancy or by surface-tension gradient in finite systems confined between horizontal poor heat conductors is introduced by Knobloch[1990] where u is the planform function,... The equation of pattern formation induced by buoyancy or by surface-tension gradient in finite systems confined between horizontal poor heat conductors is introduced by Knobloch[1990] where u is the planform function, μ is the scaled Rayleigh number, K = 1 and α represents the effects of a heat transfer finite Blot number. The cofficients β, δ and γ do not vanish when the boundary, conditions at top and bottom are not identical (β / 0, δ / 0) or nonBoussinesq effects are taked into account (γ / 0). In this paper, the Knobloch equation with α > 0 is considered, the global existence in L2-space and the finite existence time of solution in V2-space have been obtained respectively. 展开更多
关键词 Knobloch equation initial-boundary value problem blow-up global existenc
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INHOMOGENEOUS INITIAL-BOUNDARY VALUE PROBLEM FOR GINZBURG-LANDAU EQUATIONS 认领 引用 被引量：1
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作者 杨灵娥 郭柏灵 徐海祥 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第4期373-380,共8页
Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative an... Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit. 展开更多
关键词 generalized Ginzburg-Landau equation inhomogeneous initial-boundary value problem weak solution global existence
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Picard Boundary Value Problems of Second Order p-Laplacian Differential Equations 认领 引用 被引量：8
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作者 LIU Yu-ji 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期77-84,共8页
Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 ... Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper. 展开更多
关键词 solutions second order p-Laplacian differential equation two-point boundary value problem fixed-point theorem
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A NECESSARY AND SUFFICIENT CONDITION FOR SINGULAR NONLINEAR SECOND-ORDER BOUNDARY VALUE PROBLEMS TO HAVE POSITIVE SOLUTIONS 认领 引用 被引量：5
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作者 ZHAO ZENGQIN 《Applied Mathematics(A Journal of Chinese Universities)》 1998年第1期15-24,共10页
In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v, nonincrea... In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v, nonincreasing on v for each x,u; there exists a constant q∈(0,1) such that t qf(x,t -1 u,tu)f(x,u,u)λ qf(x,λ -1 u,λu),00, e(x)=G(x,x), G(x,y) is Green's function of above mentioned boundary value problem (when f(x,u,v)≡0). Received September 9,1996. Revised March 31,1997. 1991 MR Subject Classification: 34B. 展开更多
关键词 Second order boundary value problems singular differential equation necessary and sufficient condition.
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GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS 认领 引用 被引量：2
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作者 Guo Fei 《Applied Mathematics(A Journal of Chinese Universities)》 2007年第2期181-200,共20页
In this paper,the mixed initial-boundary value problem for general first order quasi-linear hyperbolic systems with nonlinear boundary conditions in the domain D={(t,x)|t≥0,x≥0}is considered.A sufficient condition t... In this paper,the mixed initial-boundary value problem for general first order quasi-linear hyperbolic systems with nonlinear boundary conditions in the domain D={(t,x)|t≥0,x≥0}is considered.A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given. 展开更多
关键词 quasilinear hyperbolic system mixed initial-boundary value problem global weakly discontinu-ous solution weak linear degeneracy
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EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION 认领 引用 被引量：2
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作者 叶耀军 《Acta Mathematica Scientia》 SCIE 2005年第4期703-709,共7页
The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div（｜△↓｜^P-2 △↓u）=｜u｜^m u, （x,t）∈[0, ＋∞）... The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div（｜△↓｜^P-2 △↓u）=｜u｜^m u, （x,t）∈[0, ＋∞） ×Ω with p 〉 2 and m 〉 0. He deals with the global solutions by D.H.Sattinger＇s potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded, the global nonexistence of solutions is verified by using the analysis method. 展开更多
关键词 Degenerate hyperbolic equations global existence and global nonexistence,initial-boundary value problem
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Simultaneous imposition of initial and boundary conditions via decoupled physics-informed neural networks for solving initialboundary value problems 认领 引用
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作者 K.A.LUONG M.A.WAHAB J.H.LEE 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2025年第4期763-780,共18页
Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static... Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost. 展开更多
关键词 decoupled physics-informed neural network(dPINN) decoupled formulation Galerkin method initial-boundary value problem(IBVP) machine learning
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POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS 认领 引用 被引量：2
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作者 LI Ren-gui +1 位作者 LI Li-shan 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第4期495-500,共6页
New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(in... New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory. 展开更多
关键词 second-order singular boundary value problems positive solutions cone fixed point
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Initial-boundary value problem of one class of nonlinear Schrdinger equations described in molecular crystals 认领 引用
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作者 房少梅 郭柏灵 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第2期139-144,共6页
In this paper, we study the initiial-boundary value problem of one class of nonlinear Schrodinger equations described in molecular crystals. Furthermore, the existence of the global solution is obtained by means of in... In this paper, we study the initiial-boundary value problem of one class of nonlinear Schrodinger equations described in molecular crystals. Furthermore, the existence of the global solution is obtained by means of interpolation inequality and a priori estimation. 展开更多
关键词 nonlinear Schrodinger equations initial-boundary value problem priori estimate global solution
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Laguerre-Gauss collocation method for initial value problems of second order ODEs 认领 引用
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作者 严建平 郭本瑜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第12期1541-1564,共24页
This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. N... This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency. 展开更多
关键词 Laguerre-Gauss collocation method initial value problem second orderODEs
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Initial-boundary value problem of nonlinear hyperbolic system for conservation laws with delta-shock waves 认领 引用 被引量：2
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作者 姚爱娣 盛万成 《Journal of Shanghai University(English Edition)》 2008年第4期306-310,共5页
For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results... For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results by taking a suitable entropy-flux pair （Journal of Differential Equations, 1988, 71（1）： 93-122）. The solutions of the initial-boundary value problem for the system are constructively obtained, in which initial-boundary data are in piecewise constant states. The delta-shock waves appear in their solutions. 展开更多
关键词 initial-boundary value problem delta-shock wave linearly degenerated entropy-flux pair entropy boundary inequality
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Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions 认领 引用 被引量：3
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作者 Nawal Abdullah Alzaid Huda Omar Bakodah 《American Journal of Computational Mathematics》 2018年第2期153-174,共22页
In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary condit... In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software. 展开更多
关键词 Decomposition Method Modified Adomian Decomposition Method Linear and Nonlinear Partial Differential Equations Mixed Boundary Conditions Initial-Boundary Value Problem
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Initial-Boundary Value Problem for Two-Component Gerdjikov–Ivanov Equation with 3 × 3 Lax Pair on Half-Line 认领 引用
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作者 朱巧珍 范恩贵 徐建 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第10期425-438,共14页
The Fokas unified method is Gerdjikov-Ivanonv equation on the half-line. expressed in terms of the solution of a 3 × 3 through the global relation.
关键词 two-component Gerdjikov-Ivanov equation initial-boundary value problem Fokas unifiedmethod Riemann-Hilbert problem
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Construction of Global Weak Entropy Solution of Initial-Boundary Value Problem for Scalar Conservation Laws with Weak Discontinuous Flux 认领 引用 被引量：1
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作者 Yihong Dai Jing Zhang 《American Journal of Computational Mathematics》 2017年第4期451-468,共18页
This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a con... This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution. 展开更多
关键词 Scalar Conservation Laws with Weak Discontinuous Flux Initial-Boundary Value Problem Elementary Wave Interaction Structure of Global Weak Entropy Solution
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Godunov's method for initial-boundary value problem of scalar conservation laws 认领 引用
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作者 林贵成 盛万成 《Journal of Shanghai University(English Edition)》 2008年第4期298-301,共4页
This paper is concerned with Godunov＇s scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov＇s scheme, which satisfies the boundary entropy condition, was given. By use of the ... This paper is concerned with Godunov＇s scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov＇s scheme, which satisfies the boundary entropy condition, was given. By use of the scheme, numerical simulation for the weak entropy solution to the initial-boundary value problem of scalar conservation laws is conducted. 展开更多
关键词 scalar conservation laws Godunov＇s method initial-boundary value problem
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ON WELL-CONDITIONED BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF SECOND ORDER DIFFERENCE EQUATIONS 认领 引用
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作者 L.Jodar E.Ponsoda M.Legua Fernandez 《Analysis in Theory and Applications》 1996年第4期81-95,共15页
In this paper well-conditioning of boundary value problems for systems of second order difference equa-tions is studied.First,a sufficient condition for the existence of a unique bounded solution (for large enough num... In this paper well-conditioning of boundary value problems for systems of second order difference equa-tions is studied.First,a sufficient condition for the existence of a unique bounded solution (for large enough number of steps) of an associated homogeneous system is given.Finally,a sufficient condition for well-condi-tioning,intrinsically related to the problem data is proposed. 展开更多
关键词 ON WELL-CONDITIONED BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF SECOND ORDER DIFFERENCE EQUATIONS
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HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS 认领 引用 被引量：6
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作者 Wang Tongke 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 2002年第2期213-225,共13页
In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference me... In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective. 展开更多
关键词 second order ordinary differential equation, two-point boundary value problem,high accuracy, finite volume element method, error estimate.
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Initial-boundary Value Problem for a Class of Quasilinear Degenerate Parabolic Equations 认领 引用
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作者 Nie Lei Xu Chaojiang 《Wuhan University Journal of Natural Sciences》 CAS 1996年第2期179-183,共5页
in this work,we study the quasilinear initial-boundary value problem , where is a system of real smooth vector fields which is defined on an open domain M of R'', and satisfies the Hormanderls condition,.Assum... in this work,we study the quasilinear initial-boundary value problem , where is a system of real smooth vector fields which is defined on an open domain M of R'', and satisfies the Hormanderls condition,.Assume that is non characteristic for the system X,,..',Xm. Under some hypothesis for the boundary of domain and the elliptic structure condition for nonlinear coerfficients Aij, Bj, C,(i, j= 1, ..', m), we have proved that the existence and regularity of solution for aboveinitialboudary value problems. 展开更多
关键词 degenerate parabolic equation vector fields non-isotropic Holder's space initial-boundary value problem
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The Third Initial-boundary Value Problem for a Class of Parabolic Monge-Ampère Equations 认领 引用
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作者 LU BO-QIANG LI FENG-QUAN 《Communications in Mathematical Research》 CSCD 2012年第1期75-90,共16页
For the more general parabolic Monge-Ampère equations defined by the operator F （D2u ＋ σ（x））, the existence and uniqueness of the admissible solution to the third initial-boundary value problem for the equa... For the more general parabolic Monge-Ampère equations defined by the operator F （D2u ＋ σ（x））, the existence and uniqueness of the admissible solution to the third initial-boundary value problem for the equation are established. A new structure condition which is used to get a priori estimate is established. 展开更多
关键词 parabolic Monge-Ampere equation admissible solution the third initial-boundary value problem
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