Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise
This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t)=A(X(t))dt+Φ(t)dBH(t), where A is a nonlinear operator satisfying some monotonicity conditions....
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/601327 |
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| _version_ | 1850174422366814208 |
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| author | Caibin Zeng Qigui Yang Junfei Cao |
| author_facet | Caibin Zeng Qigui Yang Junfei Cao |
| author_sort | Caibin Zeng |
| collection | DOAJ |
| description | This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t)=A(X(t))dt+Φ(t)dBH(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. |
| format | Article |
| id | doaj-art-d5f5d4d91ef444e580a03c5d1b28f30e |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-d5f5d4d91ef444e580a03c5d1b28f30e2025-08-20T02:19:40ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/601327601327Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian NoiseCaibin Zeng0Qigui Yang1Junfei Cao2School of Sciences, South China University of Technology, Guangzhou 510640, ChinaSchool of Sciences, South China University of Technology, Guangzhou 510640, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou 510310, ChinaThis paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t)=A(X(t))dt+Φ(t)dBH(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation.http://dx.doi.org/10.1155/2014/601327 |
| spellingShingle | Caibin Zeng Qigui Yang Junfei Cao Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise The Scientific World Journal |
| title | Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise |
| title_full | Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise |
| title_fullStr | Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise |
| title_full_unstemmed | Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise |
| title_short | Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise |
| title_sort | variational solutions and random dynamical systems to spdes perturbed by fractional gaussian noise |
| url | http://dx.doi.org/10.1155/2014/601327 |
| work_keys_str_mv | AT caibinzeng variationalsolutionsandrandomdynamicalsystemstospdesperturbedbyfractionalgaussiannoise AT qiguiyang variationalsolutionsandrandomdynamicalsystemstospdesperturbedbyfractionalgaussiannoise AT junfeicao variationalsolutionsandrandomdynamicalsystemstospdesperturbedbyfractionalgaussiannoise |