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

Pulun HouCaisheng Chen — 2011

Czechoslovak Mathematical Journal

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 - 2 u ) = u | u | β - 1 Ω | u | α d x in Ω × ( 0 , ) with zero Dirichlet boundary condition in Ω . Further, we obtain the L estimate of the solution u ( t ) and u ( t ) for t > 0 with the initial data u 0 L q ( Ω ) ( q > 1 ) , and the case α + β < m - 1 .

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