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

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＋τ in a cylinder Ω×（0, T） w...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2015, Vol.31 (1), p.123-139
Main Authors: Han, Jun Qiang, Guo, Qian Qiao
Format: Article
Language:English
Subjects:
Boundaries
Cylinders
Euclidean space
Fields (mathematics)
Inequality
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear equations
Nonlinearity
Studies
Texts
不存在性
向量
奇异
时间依赖性
时间相关
退化抛物方程
退缩抛物方程
非线性
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Summary: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＋τ in 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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-3757-z