Asymptotic behavior of a degenerate nonlocal parabolic equation

In this paper, we consider the asymptotic behavior for the degenerate nonlocal parabolic equation

     

Large time behavior of solutions to a class of doubly nonlinear parabolic equations

We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation u _t = div(u ^m−1|Du| ^p−2 Du) − u ^q with an initial condition u(x, 0) = u ₀(x). Here the exponents m, p and q satisfy m + p ⩾ 3, p > 1 and q > m + p − 2. The paper was supported by NSF of China (10571144), NSF for youth of Fujian province in China (2005J037) and NSF of Jimei University in China.     

一类反应扩散方程组的渐近行为

本文讨论了一类反应扩散方程组的渐进行为,证明了对任意ｕ〉０解在Ｃ＾ｖ（Ω）中收敛于常数平衡解,并推广了以往的结论。     

Regularity Results for a Strongly Degenerate Parabolic Equation

M. Bertsch & R. Dal Passo proved the existence and uniqueness of the Cauchy problem for u_t = (φ(u),ψ(u_x))_x, where φ > 0, ψ is a strictly increasing function with lim_{s → ∞}ψ(s) = ψ_∞ < ∞. The regularity of the solution has been obtained under the condition φ" < 0 or φ = const. In the present paper, under the condition φ" ≤ 0, we give some regularity results. We show that the solution can be classical after a finite time. Further, under the condition φ" ≤ -α_0 (where -α_0 is a constant), we prove the gradient of the solution converges to zero uniformly with respect to x as t → +∞.     

一类强退化拟线性抛物方程的弱解

In this paper, we show the existence of the renormalized solutions and the entropy solutions of a class of strongly degenerate quasilinear parabolic equations.     

LONG TIME ASYMPTOTIC BEHAVIOR OF SOLUTION OF DIFFERENCE SCHEME FOR A SEMILINEAR PARABOLIC EQUATION (I)

1.IntroductionLetfi=(0,l),f(x)eL'(fl),"o(x)EH'(fl)nHI(fl),op(u)=u',weconsiderthefollowinginitial-boundaryvalueproblem:Bytheusualapproach[1--4]wecangettheglobalexistenceofthesolutionof(1.1),furthermore,thesolutionof(l.l)convergestothesolutionofthefollowingstationaryproblem(1.2)ast-co.l)Th.ProjectissupportedbyChinaPostdoctoralFoundationandScienceFOundationofChinaAcademyofEngineeringPhysics.Inthispaperweprovethatthesolutionofimplicitdifferenceschemefor(1.1)convergestothesolutionofdifferenc…     

Traveling Wave Fronts of a Degenerate Parabolic Equation with Non-divergence Form

We study the traveling wave solutions of a nonlinear degenerate parabolic equation with non-divergence form. Under some conditions on the source, we establish the existence, and then discuss the regularity of such solutions.     

具吸附项退化抛物方程解的大时间渐近行为

对如下形式的非线性抛物方程ut=up(uu)-uq,inQ∞=Ω×(0,∞)当p<1时,讨论了其解的大时间渐近性.     

一类强退化的抛物型方程的双曲特性

MBertsch和R．DalPasso在［1］中研究了方程（其中ψ为严格增函数且为有限数）具有严格增初值的Cauchy问题．讨论了该问题的解与一阶守恒律方程的解的相似性．在[1]中，条件是一个基本假设．本文主要讨论以上方程在退化（即的情况下），相应于特殊初值的Cauchy问题的解仍具有以上双曲现象．     

一类非散度型非线性退化抛物方程解的存在性(英文)

In this paper, we discuss the existence of weak solutions to the initial and boundary value problem of a class of nonlinear degenerate parabolic equations in non-divergence form. Applying the method of parabolic regularization, we prove the existence of weak solutions to the problem. By carefully analyzing the approximate solutions to the problem, we make a series of estimates to the solutions and prove the weak convergence of the approximation solution sequence. Finally we testify the existence of weak solutions to the problem.     

Time periodic solutions of a class of degenerate parabolic equations

1.IntroductionManypapershavebeendevotedtotheexistenceoftimeperiodicsolutionsforsemilinearparabolicequations,see[1--8].Atthesametime,thestudyofquasilinearperiodic-parabolicequationsalsoattractedmanyauthors,seealso[9--141.Inparticular,recentlyHess,PozioandTesei[13]usedthemonotonicitymethodstodealwiththeequationsonot=aam a(x,t)u,wherem>1andaisafunctionperiodicint,andMizoguchi[lllappliedtheLeray-Schauderdegreetheorytoinvestigatetheequationswithsuperlinearforcingtermwherem>1,hisapositiveperiodicf…     

Vanishing solutions of anisotropic parabolic equations with variable nonlinearity

We study the property of finite time vanishing of solutions of the homogeneous Dirichlet problem for the anisotropic parabolic equations

     

Long Time Asymptotic Behavior of Solution of Difference Scheme for a Semilinear Parabolic Equation

In this paper we prove that the solution of implicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the corresponding nonlinear stationary problem as $t\rightarrow\infty$. For the discrete solution of nonlinear parabolic problem, we get its long time asymptotic behavior which is similar to that of the continuous solution. For simplicity, we consider one-dimensional problem.     

Global well-posedness for the diffusion equation of population genetics

In this paper, we study the forward diffusion equation of population genetics. We prove the global existence of smooth solutions if the initial value is smooth. We also show that if the initial value is singular on the boundary, in a weighted Sobolev space, the diffusion equation exists a unique weak solution which is a probability density function. Moreover, we investigate the asymptotic behavior of the weak solution by the entropy method.     

LONG TIME ASYMPTOTIC BEHAVIOR OF SOLUTION OF DIFFERENCE SCHEME FOR A SEMILINEAR PARABOLIC EQUATION (Ⅱ)

1.IntroductionLetfi~(0,l),f(x)EH'(fl),"o(x)EH'(fl)nHI(fl),of(u)=u3,weconsiderthefollowinginitial-boundaryvalue'problem:Bytheusualapproach[1--4]wecangettheglobalexistenceofthesolutionof(1.1),furthermore,thesolutionof(1.1)convergestothesolutionofthefollowingstationaryproblem(1.2)ast-co.l)TheProjectissupportedbyChillaPostdoctoralScienceFoundationandtheScienceFoundationofAcademyofEngineeringPhysicsofChinaIn[6]5[7]?theauthorsconsideredtheexplicitschemefor(l.l)asf(x)=0andonlytheestimateinLZf…     

反应扩散方程解的渐近性态

研究了一类反应扩散方程初始边值问题. 利用微分不等式理论得到了问题解的渐近性态.     

具Lp初值的拟线性退化抛物方程的熵解

拟线性退化抛物方程来自于反应扩散等许多物理问题,有着深刻的应用背景．本文利用Young测度的概念和Div- Curl引理证明了在0≤U0(x)∈L2(R)∩Lp(R)和f是真正非线性函数的条件下,存在一Lp熵解．