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<∞.
- Global existence
- Gradient estimate
- Quasilinear parabolic equation
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