Global and nonglobal weak solutions to a degenerate parabolic system

[摘要] This paper deals with a degenerate parabolic system coupled via general reaction terms of power type. Global weak solutions are obtained by means of energy estimates and the De Giorgi's technique. In particular, the criterion for global nonexistence of weak solutions is proved by introducing suitable weak sub-solutions together with a weak comparison principle. In summary, the critical exponent for weak solutions of the degenerate parabolic system is determined. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-01

[关键词] degenerate parabolic systems;weak sub-solutions;weak super solutions;blow-up;global existence;characteristic algebraic system;critical exponent