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.     

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.     

Blow-up for doubly degenerate nonlinear parabolic equations

In this paper, we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem of some doubly degenerate nonlinear parabolic equations. The project is supported by the Natural Science Foundation of Fujian Province of China (No. Z0511048)     

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.     

Asymptotic blow-up behavior for a nonlocal degenerate parabolic equation

In this paper, we investigate the positive solution of nonlinear degenerate equation with Dirichlet boundary condition. The blow-up criteria is obtained. Furthermore, we prove that under certain conditions, the solutions have global blow-up. When f(u)=u^p,0<p1, we gained blow-up rate estimate.     

A doubly critical degenerate parabolic problem

It is shown that the Dirichlet problem for where Ω??ⁿ is critical in that it has first eigenvalue one, is globally solvable for any continuous positive initial datum vanishing at ?Ω. Moreover, for p<3 all solutions are bounded and tend to some nonnegative eigenfunction of the Laplacian as t→∞, while if p?3 then there are both bounded and unbounded solutions. Finally, it is shown that unlike the case p∈[0,1), all steady states are unstable if p?1. Copyright © 2004 John Wiley & Sons, Ltd.     

Blow-up and extinction for a sixth-order parabolic equation

In this paper, we consider an initial-boundary value problem for a sixth-order parabolic equation. We use the modified method of potential wells to study the relationship which the equation solutions existence, blow-up and the asymptotic behavior with initial conditions.     

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)     

Semigroup approach to a doubly degenerate parabolic equation

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

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 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.

     

Global existence and nonexistence for degenerate parabolic systems

The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system

in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .

     

具有非局部源的退化奇异抛物方程组解的爆破

研究了一类新的包含幂函数和指数函数相耦合的具有非局部源的抛物方程组.用正则化的方法证明了局部解的存在唯一性,用上下解方法得到了整体存在和在有限时刻爆破的充分条件.     

Blow-up for degenerate parabolic equations with nonlocal source

This paper deals with the blow-up properties of the solution to the degenerate nonlinear reaction diffusion equation with nonlocal source in subject to the homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally or blows up in finite time are obtained. Furthermore, it is proved that under certain conditions the blow-up set of the solution is the whole domain.

     

Large time behavior of solutions to a degenerate parabolic equation not in divergence form

In this paper, we investigate positive solutions of the degenerate parabolic equation not in divergence form: ut=upΔu+auq−bur, subject to the null Dirichlet boundary condition. We at first discuss the existence and nonexistence of global solutions to the problem, and then study the large time behavior for the global solutions. When the positive source dominates the model, we prove that the global solutions uniformly tend to the positive steady state of the problem as t→∞. In particular, we establish the uniform asymptotic profiles for the decay solutions when the problem is governed by the nonlinear diffusion or absorption.     

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.     

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

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