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2011 Existence of Random Attractors for a p -Laplacian-Type Equation with Additive Noise
Wenqiang Zhao, Yangrong Li
Abstr. Appl. Anal. 2011: 1-21 (2011). DOI: 10.1155/2011/616451


We first establish the existence and uniqueness of a solution for a stochastic p -Laplacian-type equation with additive white noise and show that the unique solution generates a stochastic dynamical system. By using the Dirichlet forms of Laplacian and an approximation procedure, the nonlinear obstacle, arising from the additive noise is overcome when we make energy estimate. Then, we obtain a random attractor for this stochastic dynamical system. Finally, under a restrictive assumption on the monotonicity coefficient, we find that the random attractor consists of a single point, and therefore the system possesses a unique stationary solution.


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Wenqiang Zhao. Yangrong Li. "Existence of Random Attractors for a p -Laplacian-Type Equation with Additive Noise." Abstr. Appl. Anal. 2011 1 - 21, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1218.37070
MathSciNet: MR2817260
Digital Object Identifier: 10.1155/2011/616451

Rights: Copyright © 2011 Hindawi

Vol.2011 • 2011
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