标题：Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-Laplacian with Nonlocal Sources
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2007
卷号：2007
DOI：10.1155/2007/34301
出版社：Hindawi Publishing Corporation
摘要：This paper deals with p-Laplacian systems ut−div(|∇u|p−2∇u)=∫Ωvα(x, t)dx, x∈Ω, t>0, vt−div(|∇v|q−2∇v)=∫Ωuβ(x,t)dx, x∈Ω, t>0, with null Dirichlet boundary conditions in a smooth bounded domain
Ω⊂ℝN, where p,q≥2, α,β≥1. We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow up estimates for above p-Laplacian systems with the homogeneous Dirichlet boundary value conditions are obtained under Ω=BR={x∈ℝN:|x|<R} (R>0). Then under appropriate hypotheses, we establish local theory of the
solutions and obtain that the solutions either exist globally or blow up in finite time.
