一类双重退化抛物方程重整化解的稳定性

讨论了一类有双重退化性的抛物方程的Cauchy问题,并基于Kruzhkov技术,证明了重整化解的稳定性.     

Semigroup approach to a doubly degenerate parabolic equation

1.IntroductionWeareconcernedwiththesemigroupapproachtotheinitialvalueproblemfordoublynonlineardegenerateparabolicequationoftheformwhicharisesfromdifferentphysicalbackgroundssuchasthemodelingofthemotionofnon-Newtonianfluids.Inthepastyears,thenonlinear...     

The approximating behavior on nonlinearities of solutions of a degenerate parabolic equation

The approximating character of solutions of a degenerate parabolicequation is studied in this paper. We will show that the solutionsare Lipschitz continuous with respect to the nonlinearitiesof the equations. An explicitly approximating estimate is obtained.     

EXISTENCE，UNIQUENESS AND PROPERTIES OF THE SOLUTIONS OF A DEGENERATE PARABOLIC EQUATION WITH DIFFUSION－ADVECTION－ABSORPTION

ＥＸＩＳＴＥＮＣＥ，ＵＮＩＱＵＥＮＥＳＳＡＮＤＰＲＯＰＥＲＴＩＥＳＯＦＴＨＥＳＯＬＵＴＩＯＮＳＯＦＡＤＥＧＥＮＥＲＡＴＥＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＷＩＴＨＤＩＦＦＵＳＩＯＮ－ＡＤＶＥＣＴＩＯＮ－ＡＢＳＯＲＰＴＩＯＮ￥ＳＯＮＧＢＩＮＨＥＮＧ（宋...     

Asymptotic behavior of a degenerate nonlocal parabolic equation

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

     

Homogenization of a nonlinear degenerate parabolic differential equation

This paper is devoted to the homogenization of a nonlinear degenerate parabolic problem ɑtu∈-div(D(x/∈, u∈,▽u∈)+ K(x/∈, u∈))= f(x) with Dirichlet boundary condition. Here the operator D(y, s,s) is periodic in y and degenerated in ▽s. In the paper, under the two-scale convergence theory, we obtain the limit equation as ∈→ 0 and also prove the corrector results of ▽u∈ to strong convergence.     

On a double degenerate fourth-order parabolic equation

The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit.     

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…     

Cauchy problem for a degenerate parabolic equation with non-divergence form

In this article, it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form.     

Localization for a doubly degenerate parabolic equation with strongly nonlinear sources

In this paper, we study the strict localization for the doubly degenerate parabolic equation with strongly nonlinear sources, We prove that, for non‐negative compactly supported initial data, the strict localization occurs if and only if q?m(p?1). Copyright © 2009 John Wiley & Sons, Ltd.     

BV solutions of a singular diffusion equation

In this paper, we study discontinuous solutions of a partial differential equation of strongly degenerate parabolic type. A notion of weak solutions of BV class is proposed, and existence and uniqueness results are obtained.     

退缩抛物型方程解的熄灭时间

证明了一类退缩抛物型方程解在有限时刻熄灭,并对解的熄灭时间进行估计     

ON THE CAUCHY PROBLEM OF NONLINEAR DEGENERATE PARABOLIC EQUATION

ＯＮＴＨＥＣＡＵＣＨＹＰＲＯＢＬＥＭＯＦＮＯＮＬＩＮＥＡＲＤＥＧＥＮＥＲＡＴＥＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮ￥ＹＡＮＧＪＩＮＳＨＵＮＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｐｒｏｖｅｔｈｅｅｘｉｓｔｅｎｃｅｏｆｓｏｌｕｔｉｏｎｏｆｔｈｅＣａ...     

On the behavior of solutions to the Cauchy problem for a degenerate parabolic equation with inhomogeneous density and a source

The Cauchy problem for a degenerate parabolic equation with a source and inhomogeneous density of the form

$\rho (x)\frac{{\partial u}}{{\partial t}} = div(u^{m - 1} \left| {Du} \right|^{\lambda - 1} Du) + \rho (x)u^p $

is studied. Time global existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of the solution are obtained in the case of global solvability.

     

一类含非局部源的非线性退化抛物型方程

The global existence and finite time blow up of the positive solution for a nonlinear degenerate parabolic equation with non-local source are studied.     

On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources

In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||_f||| _h and 〈f〉_h, we give the sufficient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered. This work was supported by the National Natural Science Foundation of China (Grant No. 10531020)     

Regularity of viscosity solutions of a degenerate parabolic equation

We study the Cauchy problem for the nonlinear degenerate parabolic equation of second order

and present regularity results for the viscosity solutions.

     

Blow-up for a degenerate parabolic equation with nonlocal source and nonlocal boundary

In this article, we investigate the blow-up properties of the positive solutions for a doubly degenerate parabolic equation with nonlocal source and nonlocal boundary condition. The conditions on the existence and nonexistence of global positive solutions are given. Moreover, we give the precise blow-up rate estimate and the uniform blow-up estimate for the blow-up solution.