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Existence of Random Attractors for a ð ‘ -Laplacian-Type Equation with Additive Noise

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  • Wenqiang Zhao
  • Yangrong Li

Abstract

We first establish the existence and uniqueness of a solution for a stochastic ð ‘ -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.

Suggested Citation

  • Wenqiang Zhao & Yangrong Li, 2011. "Existence of Random Attractors for a ð ‘ -Laplacian-Type Equation with Additive Noise," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-21, June.
    • Handle: RePEc:hin:jnlaaa:616451
    DOI: 10.1155/2011/616451
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