THE HEAT EQUATION IN R WITH ANTI-PERIODIC BOUNDARY CONDITION

1Intr0ducti0nThispaPerdeaIswiththef0llowingproblerns:whereTisanypositivenumberandaisarealnumberwithIal31.In[1],A.Pazydiscussedtheproblelnasfollows:Heobtainedtheexistenceanduniqueness0fthesolutionfor(P3)intl1espaceC[0,1lundersomehypotheses0nf.(P3)isannonlinearheatequati0nwithinitialconditionandperi0dicboundaryc0nditi0n.Recentlysomeauthorshavediscussedsomedtherentialequationswithantiperi0dicboundarycondition8([2],[3]).However,theyonlystudiedtheclassicalsolutionslikewhatA.Pazydidforperiodicb…     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

The purpose of this paper is to investigate the stability and asymptotic behav-ior of the time-dependent solutions to a linear parabolic equation with nonlinear boundarycondition in relation to their corresponding steady state solutions. Then, the above resultsare extended to a semilinear parabolic equation with nonlinear boundary condition by an-alyzing the corresponding eigenvalue problem and using the method of upper and lowersolutions.     

一类非线性双曲型方程有限元方法的误差分析

关于二阶双曲型方程有限元方法的理论研究,已有不少工作,如[1]—[5]。[5]对具Dirichlet边界条件且初边值均取0值的一类非线性双曲方程定解问题的有限元方法,导出了H~1-逼近阶估计,其中,对有关辅助函数u([5],p,151)施加了||?u||_(L~∞(Ω×[0,T]))< ∞的假定。 本文对[5]中研究过的方程,就Dirichlet边界及第三类边界两种情况,给出了半离散Galerkin方法H~1及L~2误差估计。得到的逼近阶都是最佳的,而且,在建立H~1估计的     

一类非线性方程奇摄动问题的激波解

利用匹配条件，讨论了一类非线性奇摄动问题的激波解，得出了激波解与边界条件的对应关系。     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF STRONGLY NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the singularly perturbed theory and the boundary layer corrective method, the asymptotic behavior of solution for a class of strongly nonlinear non-autonomous equations and the infection for asymptotic behavior of the solution with regard to the boundary condition are studied. According to the different regions of the boundary value, the asymptotic expansions of the solution for the original problem are obtained simply and conveniently.     

A NONLOCAL NONLINEAR BOUNDARYVALUE PROBLEM FOR THE HEAT EQUATIONS

51.IntroductionandMalnResultsLetflCR"(n=2or3)beaboundedsmoothdomainwithboundaryan=r1ur2,wherer1nr2=Oandr1,r2/O.Weconsiderthefollowingmixedinitial-boundaryvalueproblemfortheheatequation'whereH'DHCR-Risastrict1ydecreasingtunction,ustancnormalvectorattheboundary.Theboundaryconditiononr2appearsinthermistors.Howison,RodriguesandShillorl1]studiedsuchkindofboundaryvalueproblemforellipticequations.HerewesupposethatHisonto'nH=R,andwherea,bdenote,andwillalwaysdenote,varieskindofconstants.Underhy…     

带非线性边界的非线性双曲型方程的有限元素法分析

带非线性边界的非线性双曲型方程的有限元素法分析李潜（山东师范大学数学系）魏洪（中国人民公安大学科技部）ＴＨＥＦＩＮＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＦＯＲＮＯＮＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＷＩＴＨＮＯＮＬＩＮＥＡＲＢＯＵＮＤＡＲＹＣ...     

一类非线性奇摄动系统的可解性及渐近解

研究了一类非线性微分系统的奇摄动边值问题.利用边界层校正法构造了形式渐近解和用微分不等式理论,证明了解的渐近展开式的一致有效性,得到了相应的定理,从而得到了原问题的可解性条件.     

THE MIXED PROBLEM FOR A CLASS OF NONLINEAR SYMMETRIC HYPERBOLIC SYSTEMS WITH DISCONTINUOUS DATA

1IntroductionAs we well know,the study of the local existence of discontinuous solutions to semilinearor quasi-linear hyperbolic systems in higher dimension spaces has attracted considerable at-tention of many well-known mathematicians,thanks to A.Majda’…     

Three positive solutions for the one-dimensional p-Laplacian

In this paper, nonlinear two point boundary value problems with p-Laplacian operators subject to Dirichlet boundary condition and nonlinear boundary conditions are studied. We show the existence of three positive solutions by the five functionals fixed point theorem.     

A coherent analysis of Stokes flows under boundary conditions of friction type

This paper is concerned with the stationary and nonstationary flow of viscous incompressible fluid under boundary conditions of friction type, which are certain nonlinear boundary conditions similar to the so-called Signorini boundary condition in elasticity. We assume that the flow is governed by the linear Stokes equation, while the boundary condition is nonlinear. From the methodological viewpoint, the analysis is carried out in a coherent way, starting from study of the related boundary value problems for the stationary flow by means of the theory of variational inequalities, and getting to wellposedness of the initial boundary value problems for the nonstationary flow by means of the nonlinear semigroup theory. From the viewpoint of applications, we mention original motivations and include some new generalizations like the cases of anisotropic friction and inhomogeneous boundary value.     

QUENCHING ON BOUNDARY TO THE NEWTON FILTRATION EQUATION(Ⅰ)

This paper discusses the global existence and quenching of the solution tothe Newton filtration equation with the nonlinear boundary condition. The authors alsodiscuss the profile of the quenching solution in the quenching time and obtain the quenchingrate of the quenching solution.     

QUENCHING ON BOUNDARY TO THE NEWTON FILTRATION EQUATION (I)

This paper discusses the global existence and quenching of the solution to the Newton filtration equation with the nonlinear boundary condition. The authors also discuss the profile of the quenching solution in the quenching time and obtain the quenching rate of the quenching solution.     

滑动支撑的弹性梁静态方程的可解性

给出了滑动支撑的弹性梁静态方程可解的一组两参数非共振条件。     

Concentrated terms and varying domains in elliptic equations: Lipschitz case

In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior, which is uniformly Lipschitz and nonlinear terms, are concentrated in a region, which neighbors the boundary of domain. We prove that this family of solutions converges to the solutions of a limit problem in H¹an elliptic equation with nonlinear boundary conditions which captures the oscillatory behavior of the boundary and whose nonlinear terms are transformed into a flux condition on the boundary. Indeed, we show the upper semicontinuity of this family of solutions.Copyright © 2015 John Wiley & Sons, Ltd.     

SEMIDISCRETIZATION IN SPACE OF NONLINEAR DEGENERATE MRABOLIC EQUATIONS WITH BLOW-UP OF THE SOLUTIONS

1. IntroductionLet n be a bounded domain in AN with smooth boundary Off. We consider thefollowing initial boundary value problem:where 6, p are positive constants and "o(x) is a nonnegative bounded continuous function on fi.When N = 1 and 5 ~ 2, the problem arises in a model for the resistive diffusion of aforce--free magnetic field in a plasma confined between two walls in one dimension (see[5], [8], [9], [10] and [14]). Equation (1) also describes the evolution of the curvatureof a locally…     

Oblique boundary value problems for equations of Monge-Ampère type

We prove the existence of classical solutions of elliptic equations of Monge-Ampère type subject to a semilinear oblique boundary condition which is a perturbation of the Neumann boundary condition. Our techniques also allow us to treat fully nonlinear strictly oblique boundary conditions satisfying a concavity condition. Examples show that the above restrictions on the boundary condition are generally necessary for the existence of classical solutions. Received May 22, 1996 / Accepted April 10, 1997     

Multiple positive solutions for a class of semilinear elliptic systems with nonlinear boundary condition

Two positive solutions are obtained for the nonlinear homogeneous system with nonlinear homogeneous boundary condition via the Nehari manifold approach.     

Bifurcation of positive solutions to scalar reaction–diffusion equations with nonlinear boundary condition

The bifurcation of non-trivial steady state solutions of a scalar reaction–diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.     

非局部初边值条件下的抛物型偏微分方程

本文讨论在非局部初边值条件下的抛物型偏微分方程,在更为宽松的边界假设条件下讨论所构造的迭代序列的收敛速度问题.并且对非局部初值条件为离散形式的情况做了相应的讨论.