In this paper, we prove the existence of solution of the Cauchy problem of a nonlinear degenerate parabolic equation. Moreover some regularizing effects are exhibited.
In this paper, we study the nonexistence and longtime behavior of weak solution for the degenerate parabolic equation σtun=umdiv（｜▽um｜p-2▽um）＋γ｜▽um｜p＋βun with zero boundary condition. Blow-up time is der...In this paper, we study the nonexistence and longtime behavior of weak solution for the degenerate parabolic equation σtun=umdiv（｜▽um｜p-2▽um）＋γ｜▽um｜p＋βun with zero boundary condition. Blow-up time is derived when the blow-up does occur.展开更多
In this paper, we are concerned with the following three types of nonlinear degenerate parabolic equations with time-dependent singular potentials： uq/ t=▽α·（‖z‖^-pγ｜▽αu｜^p-2▽αu）＋V（z, t）u^p-1, uq...In this paper, we are concerned with the following three types of nonlinear degenerate parabolic equations with time-dependent singular potentials： uq/ t=▽α·（‖z‖^-pγ｜▽αu｜^p-2▽αu）＋V（z, t）u^p-1, uq/ t=▽α·（‖z‖^-2γ▽αu^m）＋V（z, t）u^m, uq/ t=u^μ▽α·（u^τ｜▽αu｜^p-2▽αu）＋V（z, t）u^p-1＋μ＋τin a cylinder Ω×（0, T） with initial condition u（z, 0）=u0（z） ≥ 0 and vanishing on the boundary Ω×（0, T）, where Ω is a Carnot-Carathéodory metric ball in Rd＋k and the time-dependent singular potential function is V（z, t） ∈ L^1loc （Ω×（0, T））. We investigate the nonexistence of positive solutions of these three problems and present our results on nonexistence.展开更多
The purpose of this paper is to investigate the nonexistence of positive so lutions of the following doubly nonlinear degenerate parabolic equations:{∂u=▽k·(u^(m-1)|▽ku|^(p-2)▽ku)+(w)u^(m+p-2),u(w,0)=u0(w)≥0,...The purpose of this paper is to investigate the nonexistence of positive so lutions of the following doubly nonlinear degenerate parabolic equations:{∂u=▽k·(u^(m-1)|▽ku|^(p-2)▽ku)+(w)u^(m+p-2),u(w,0)=u0(w)≥0,u(w,t)=0,inΩ×(0,T),inΩ,on∂Ω×(0,T),where Q is a Carnot-Carathéodory metric bal in IR^(2n+1)generated by Greiner vector fields,V∈L_(loc)(Ω),k∈N,m∈R,1<p<2n+2k and m+p-2>0.The better lower bound p*for m+p is found and the nonexistence results are proved for p*≤m+p<3.展开更多
In this paper, we obtain the necessary and sufficient conditions on the global existence of all positive （weak） solutions to a nonlinear degenerate parabolic equation with nonlinear boundary condition.
This paper studies the conditions of blow up in finite time of solutions of initial boundary value problem for a class nonlinear doubly degenerate parabolic equation.
This paper is devoted to the homogenization of a nonlinear degenerate parabolic problemwith Dirichlet boundary condition. Here the operator D（y, s, △s） is periodic in y and degenerated in △s. In the paper, under t...This paper is devoted to the homogenization of a nonlinear degenerate parabolic problemwith 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.展开更多
文摘In this paper, we prove the existence of solution of the Cauchy problem of a nonlinear degenerate parabolic equation. Moreover some regularizing effects are exhibited.
基金Supported by the National Nature Science Foundation of China(Grant No.7117116411426176)Foundation of Guizhou Science and Technology Department(Grant No.[2015]2076)
文摘In this paper, we study the nonexistence and longtime behavior of weak solution for the degenerate parabolic equation σtun=umdiv（｜▽um｜p-2▽um）＋γ｜▽um｜p＋βun with zero boundary condition. Blow-up time is derived when the blow-up does occur.
基金Supported by Nature Science Fund of Shaanxi Province(Grant No.2012JM1014)
文摘In this paper, we are concerned with the following three types of nonlinear degenerate parabolic equations with time-dependent singular potentials： uq/ t=▽α·（‖z‖^-pγ｜▽αu｜^p-2▽αu）＋V（z, t）u^p-1, uq/ t=▽α·（‖z‖^-2γ▽αu^m）＋V（z, t）u^m, uq/ t=u^μ▽α·（u^τ｜▽αu｜^p-2▽αu）＋V（z, t）u^p-1＋μ＋τin a cylinder Ω×（0, T） with initial condition u（z, 0）=u0（z） ≥ 0 and vanishing on the boundary Ω×（0, T）, where Ω is a Carnot-Carathéodory metric ball in Rd＋k and the time-dependent singular potential function is V（z, t） ∈ L^1loc （Ω×（0, T））. We investigate the nonexistence of positive solutions of these three problems and present our results on nonexistence.
基金support from Nature Science Fund of China(No.11771354).
文摘The purpose of this paper is to investigate the nonexistence of positive so lutions of the following doubly nonlinear degenerate parabolic equations:{∂u=▽k·(u^(m-1)|▽ku|^(p-2)▽ku)+(w)u^(m+p-2),u(w,0)=u0(w)≥0,u(w,t)=0,inΩ×(0,T),inΩ,on∂Ω×(0,T),where Q is a Carnot-Carathéodory metric bal in IR^(2n+1)generated by Greiner vector fields,V∈L_(loc)(Ω),k∈N,m∈R,1<p<2n+2k and m+p-2>0.The better lower bound p*for m+p is found and the nonexistence results are proved for p*≤m+p<3.
基金supported by the NSFC(Grant No.10471009)BSFC(Grant No.1052001)
文摘In this paper, we obtain the necessary and sufficient conditions on the global existence of all positive （weak） solutions to a nonlinear degenerate parabolic equation with nonlinear boundary condition.
文摘This paper studies the conditions of blow up in finite time of solutions of initial boundary value problem for a class nonlinear doubly degenerate parabolic equation.
基金supported by National Natural Science Foundation of China (Grant No. 10871190)the Qing-Lan Project of Jiangsu Province
文摘This paper is devoted to the homogenization of a nonlinear degenerate parabolic problemwith 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.
