Global Existence and Gradient Estimates for the Quasilinear Parabolic Equations of m-Laplacian Type with a Nonlinear Convection Term

In this paper, we derive precise estimates for u(t) including smoothing effects near t=0 and decay as t→∞ as well as global existence of the solutions u(t) to the initial-boundary value problem in a bounded domain in Rn for the quasilinear parabolic equation of the m Laplacian type with a nonlinear convection term b(u) u. For the initial data u0 we only assume u0 Lq(Ω), 1 q<∞.