Global existence and blow-up solutions for doubly degenerate parabolic system with nonlocal source

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:374

Article

Wang, Jian

关键词: Non-Newton;    Doubly degenerate;    System;    Nonlocal;    Global existence;    Blow-up;   

DOI  :  10.1016/j.jmaa.2010.08.078

来源: Elsevier

【 摘 要 】

This paper deals with the following nonlocal doubly degenerate parabolic system u(t) - div(vertical bar del(m)(u)vertical bar(p-2)del u(m)) = a integral(Omega)u(alpha 1)(x, t)v(beta 1)(x, t)dx, v(t) - div(vertical bar del v(n)vertical bar(q-2)del v(n)) = b integral(Omega)u(alpha 2)(x, t)v(beta 2)(x, t)dx with null Dirichlet boundary conditions in a smooth bounded domain Omega subset of R(N), where m, n >= 1, p,q > 2, alpha(i), beta(i) >= 0, i = 1.2 and a, b > 0 are positive constants. We first get the non-existence result for a related elliptic systems of non-increasing positive solutions. Secondly by using this non-existence result, blow-up estimates for above non-Newton polytropic filtration systems with the homogeneous Dirichlet boundary value conditions are obtained. Then under appropriate hypotheses, we establish local theory of the solutions and prove that the solution either exists globally or blows up in finite time. In the special case, beta(1) = n(q - 1) - beta(2), alpha(2) = m(p - 1) - alpha(1), we also give a criterion for the solution to exist globally or blow up in finite time, which depends on a, b and zeta(x), theta(x) as defined in the main results. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free