Global existence and gradient estimates for the quasilinear parabolic equations of m-Laplacian type with a nonlinear convection term

摘要

In this paper, we derive precise estimates for del u(t) including smoothing effects near t=0 and decay as t --> infinity as well as global existence of the solutions u(t) to the initial-boundary value problem in a bounded domain in R-n for the quasilinear parabolic equation of the m Laplacian type with a nonlinear convection term b(u) del u. For the initial data u(0) we only assume u(0) epsilon L-q(Omega), 1 less than or equal to q < infinity. (C) 2000 Academic Press. [References: 21]