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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
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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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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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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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THE SECOND INITIAL-BOUNDARY VALUE PROBLEM FOR A QUASILINEAR PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS 认领 引用
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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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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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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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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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Initial-boundary Value Problem for a Class of Quasilinear Degenerate Parabolic Equations 认领 引用
10
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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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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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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SINGULAR PERTURBATION OF INITIAL-BOUNDARY VALUE PROBLEMS FOR A CLASS OF REACTION DIFFUSION SYSTEMS 认领 引用 被引量：4
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作者 莫嘉琪 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第4期399-408,共10页
In this paper, a class of singularly perturbed initial-boundary value problems for the reaction diffusion systems is considered. Using the theory of differential inequality, we prove that the initial-boundary value pr... In this paper, a class of singularly perturbed initial-boundary value problems for the reaction diffusion systems is considered. Using the theory of differential inequality, we prove that the initial-boundary value problems have a solution and obtain their asymptotic expansion. 展开更多
关键词 Mathematical Techniques Boundary Value Problems
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AN EXPONENTIALLY FITTED DIFFERENCE SCHEME FOR THE HYPERBOLIC-HYPERBOLIC SINGULARLY PERTURBED INITIAL-BOUNDARY VALUE PROBLEM 认领 引用
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作者 苏煜城 林平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第3期237-245,共9页
In this paper we discuss, an initial-boundary value problem of hyperbolic type with first derivative with respect to x. The asymptotic solution is constructed and its uniform validity is proved under weader compatibil... In this paper we discuss, an initial-boundary value problem of hyperbolic type with first derivative with respect to x. The asymptotic solution is constructed and its uniform validity is proved under weader compatibility conditions. Then we develop an exponentially fitted difference scheme and establish discrete energy inequality. Finally, we prove that the solution of difference problem uniformly converges to the solution of the original problem. 展开更多
关键词 hyperbolic equation singular perturbation exponential fitting,difference scheme boundary value problem
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INITIAL-BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM FOR A QUASILINEAR EVOLUTION EQUATION 认领 引用 被引量：2
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作者 杨志坚 《Acta Mathematica Scientia》 SCIE 1999年第S1期487-496,共10页
In the present paper,the local existence of classical solutions to the periodic boundary problem and the Cauchy problem of a quasilinear evolution equation are studied under the assumptions that do not require the mon... In the present paper,the local existence of classical solutions to the periodic boundary problem and the Cauchy problem of a quasilinear evolution equation are studied under the assumptions that do not require the monotonicity of σi(s) (i= 1,…, n). The nonexistence of global solutions to the initial-boundary value problem of the equation is also discussed, a blowup theorem is proved and a concrete example is given. 展开更多
关键词 Initial-boundary value problem Cauchy problem quasilinear evolution equation local solution blowup
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NONLINEAR RIEMANN AND HILBERT BOUNDARY VALUE PROBLEMS WITH SQUARE ROOTS IN VARIABLE EXPONENT SPACES 认领 引用
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作者 Yajun Hu Fuli He 《Acta Mathematica Scientia》 SCIE CSCD 2026年第1期1-18,共18页
In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zer... In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces. 展开更多
关键词 boundary value problem Cauchy-type integral variable exponent spaces non-linearity piecewise Lyapunov curve
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The Well and Box Types Initial Value Problems of the Defocusing mKdV Equation 认领 引用
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作者 Yuhan Ye Juanjuan Wu 《Chinese Physics Letters》 SCIE EI CAS CSCD 2026年第4期1-6,共6页
We study the time evolution problems of special initial values with two discontinuities for the defocusing mKdV equation.Based on the finite-gap integral method,Whitham modulation system of the defocusing m Kd V equat... We study the time evolution problems of special initial values with two discontinuities for the defocusing mKdV equation.Based on the finite-gap integral method,Whitham modulation system of the defocusing m Kd V equation is derived in the form of Riemann invariants,and full-time evolution results for six types of initial values with two discontinuities are obtained in detail.The regions where rarefaction waves interact with dispersive shock waves are thoroughly analyzed.Two novel phenomena,namely soliton trains and linear wave packets,are identified and their intrinsic mechanisms are systematically illustrated.All the results are verified by numerical simulations. 展开更多
关键词 time evolution problems soliton trai box type initial value problems dispersive shock waves well type initial value problems rarefaction waves defocusing m kd v equation riemann invariantsand
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An Initial-Boundary Value Problem for a Modified Transitional Korteweg-de Vries Equation 认领 引用
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作者 Charles Bu 《Journal of Applied Mathematics and Physics》 2025年第1期138-147,共10页
We study the following modified transitional Korteweg-de Vries equation ut+f(t)upux+uxxx=0, (x,t)∈R+×R+, (p≥2is an even integer) with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t... We study the following modified transitional Korteweg-de Vries equation ut+f(t)upux+uxxx=0, (x,t)∈R+×R+, (p≥2is an even integer) with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Under the conditions either (i) f(t)≤0, f′(t)≥0or (ii) f(t)≤−αwhere α>0, we prove the existence of a unique global classical solution. 展开更多
关键词 Modified Transitional KdV Equation Initial-Boundary Value Problem Semi-Group Local and Global Existence
Nonlocal Boundary Value Problems for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval 认领 引用
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作者 ZHENG Yanping YANG Hui WANG Wenxia 《应用数学》 北大核心 2026年第2期360-372,共13页
This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theo... This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results. 展开更多
关键词 Boundary value problem Disturbance parameter Infinite interval Bifurcation point Cone
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