Global existence and blowup solutions for quasilinear parabolic equations

The authors discuss the quasilinear parabolic equation ut = ∇ · (g(u)∇u) + h(u,∇u) + f (u) with u|∂Ω = 0, u(x, 0) = φ(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 − in Ω with Dirichlet boundary condition. For a special case, they obtain a sharp result. © 2007 Elsevier Inc. All rights reserved