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

By Mitsuhiro T. Nakao, Caisheng Chen. 2000

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Abstract 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 R n for the quasilinear parabolic equation of the m Laplacian type with a nonlinear convection term b ( u ) ∇ u . For the initial data u 0 we only assume u 0 ∈ L q ( Ω ), 1⩽ q

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/397becee1e5364de46afdf9db8f5a7244e3f20c6