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Czechoslovak Mathematical Journal

, Volume 61, Issue 2, pp 389–400 | Cite as

L Estimates of solution for m-Laplacian parabolic equation with a nonlocal term

  • Pulun Hou
  • Caisheng Chen
Article
  • 62 Downloads

Abstract

In this paper, we consider the global existence, uniqueness and L estimates of weak solutions to quasilinear parabolic equation of m-Laplacian type u t − div(|∇u| m−2u) = u|u| β−1Ω |u| α dx in Ω × (0,∞) with zero Dirichlet boundary condition in tdΩ. Further, we obtain the L estimate of the solution u(t) and ∇u(t) for t > 0 with the initial data u 0L q (Ω) (q > 1), and the case α + β < m − 1.

Keywords

m-Laplacian parabolic equations global existence uniqueness L estimates 

MSC 2010

35K65 35K92 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2011

Authors and Affiliations

  1. 1.Department of MathematicsHohai UniversityNanjingP.R. China

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