Existence of Solutions for the Evolution p(x)‐Laplacian Equation Not in Divergence Form

Changchun Liu, Junchao Gao and Songzhe Lian

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: The existence of weak solutions is studied to the initial Dirichlet problem of the equation ut = udiv(|∇u|p(x)−2∇u), with inf p(x) > 2. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.

Date: 2012
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https://doi.org/10.1155/2012/835495

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:835495

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