Existence of Random Attractors for a p-Laplacian-Type Equation with Additive Noise
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 obstac...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/616451 |
| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |