摘要
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.
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
Supported by Nature Science Fund of Shaanxi Province(Grant No.2012JM1014)
