一类带有非线性源的P-Laplacian方程解的熄灭和不熄灭问题

Extinction and Non-extinction of a P-Laplacian Equation with a Nonlinear Source

主要利用了比较原理和Hlder不等式以及Sobolev嵌入不等式,研究了方程u/t=div(|▽u|p-2▽u)+f(u)在初值u0(x)∈c(Ω)∩w1,p0(Ω)和零边值条件下的熄灭和不熄灭性.

By using comparison principle,H（O）lder inequality and sobolev embedding inequality,this thesis has studied if the equation（（θ）u/（θ）t =div（｜ ▽ u ｜p-2 ▽ u） ＋f（u））has extinction or non-extinction traits under the condition of initial value（u0 （x） ∈ c（Ω） ∩ w10,p） boundary value.