Homogeneous Dirichlet condition of an anisotropic degenerate parabolic equation

The well-posedness of an anisotropic parabolic equation based on the partial boundary value condition

Boundary Estimates for a Degenerate Parabolic Equation with Partial Dirichlet Boundary Conditions

We study the boundary regularity properties and derive pointwise a priori supremum estimates of weak solutions and their derivatives in terms of suitable weighted L-norms for a class of degenerate parabolic equations that satisfy homogeneous Dirichlet boundary conditions on certain portions of the boundary. Such equations arise in population genetics in the study of models for the evolution of ...

Blow up problems for a degenerate parabolic equation with nonlocal source and nonlocal nonlinear boundary condition

* Correspondence: zhgs917@163. com Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, China Full list of author information is available at the end of the article Abstract This article deals with the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. The blow-up and globa...

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

The purpose of this work is to deal with the blow-up behavior of the nonnegative solution to a degenerate and singular parabolic equation with nonlocal boundary condition. The conditions on the existence and non-existence of the global solution are given. Further, under some suitable hypotheses, we discuss the blow-up set and the uniform blow-up profile of the blow-up solution. c ©2016 All righ...

The geometric properties of a degenerate parabolic equation with periodic source term

In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. Our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete Riemannian manifold floating in space RN+1and is tangent to the space RN at ∂H0(t); (2...