Nonlinear Degenerate Parabolic Equations with Time-dependent Singular Potentials for Baouendi–Grushin Vector Fields

被引：0

作者：

Jun Qiang HAN ^{[1
]}

Qian Qiao GUO ^{[1
]}

机构：

[1] Department of Applied Mathematics, Northwestern Polytechnical University

来源：

Acta Mathematica Sinica,English Series | 2015年 / 01期

关键词：

Nonlinear degenerate parabolic equations; Baouendi–Grushin vector fields; positive solutions; nonexistence; Hardy inequality;

D O I：

暂无

中图分类号：

O175.26 [抛物型方程];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the following three types of nonlinear degenerate parabolic equations with time-dependent singular potentials:a uqa t= aα· z-pγ|aαu|p-2 aαu+ V(z, t) up-1,a uq a t= aα· z-2γaαum + V(z, t) um,a uqa t= uμ aα·uτ|aαu|p-2 aαu+ V(z, t) up-1+μ+τin a cylinder Ω×(0, T) with initial condition u(z, 0) = u0(z) ≥ 0 and vanishing on the boundarya Ω×(0, T), where Ω is a Carnot–Carath′eodory metric ball in Rd+kand the time-dependent singular potential function is V(z, t) ∈ L1loc(Ω×(0, T)). We investigate the nonexistence of positive solutions of these three problems and present our results on nonexistence.

引用

页码：123 / 139

页数：17

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