Global existence and blowup solutions for quasilinear parabolic equations

Abstract

The authors discuss the quasilinear parabolic equation u(t) = del . (g(u)del u) + h(u, del u) + f(u) with u vertical bar(partial derivative Omega) = 0, u(x, 0) = phi (x). If f, g and h are polynomials with proper degrees and proper coefficients, they show that the blowup property only depends on the first eigenvalue of -Delta in Omega with Dirichlet boundary condition. For a special case, they obtain a sharp result. (C) 2007 Elsevier Inc. All rights reserved.