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

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

The existence of weak solutions is studied to the initial Dirichlet problemof 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 solu...

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Veröffentlicht in:Journal of Applied Mathematics 2012-01, Vol.2012 (2012), p.1561-1581-690
Hauptverfasser: Liu, Changchun, Lian, Songzhe, Gao, Junchao
Format: Artikel
Sprache:eng
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Zusammenfassung:The existence of weak solutions is studied to the initial Dirichlet problemof 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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2012/835495