Uniform Large Deviation Principles of Fractional Reaction-Diffusion Equations Driven by Superlinear Multiplicative Noise on R^n
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910485057634304 |
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| author | Wang, Bixiang |
| author_facet | Wang, Bixiang |
| contents | In this paper, we investigate the uniform large deviation principle of the fractional stochastic reaction-diffusion equation on the entire space R^n as the noise intensity approaches zero. The nonlinear drift term is dissipative and has a polynomial growth of any order. The nonlinear diffusion term is locally Lipschitz continuous and has a superlinear growth rate. By the weak convergence method, we establish the Freidlin-Wentzell uniform large deviations over bounded initial data as well as the Dembo-Zeitouni uniform large deviations over compact initial data. The main difficulties are caused by the superlinear growth of noise coefficients and the non-compactness of Sobolev embeddings on unbounded domains. The dissipativeness of the drift term and the idea of uniform tail-ends estimates of solutions are employed to circumvent these difficulties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08722 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform Large Deviation Principles of Fractional Reaction-Diffusion Equations Driven by Superlinear Multiplicative Noise on R^n Wang, Bixiang Probability Analysis of PDEs 60F10, 60H15, 37L55, 35R60 In this paper, we investigate the uniform large deviation principle of the fractional stochastic reaction-diffusion equation on the entire space R^n as the noise intensity approaches zero. The nonlinear drift term is dissipative and has a polynomial growth of any order. The nonlinear diffusion term is locally Lipschitz continuous and has a superlinear growth rate. By the weak convergence method, we establish the Freidlin-Wentzell uniform large deviations over bounded initial data as well as the Dembo-Zeitouni uniform large deviations over compact initial data. The main difficulties are caused by the superlinear growth of noise coefficients and the non-compactness of Sobolev embeddings on unbounded domains. The dissipativeness of the drift term and the idea of uniform tail-ends estimates of solutions are employed to circumvent these difficulties. |
| title | Uniform Large Deviation Principles of Fractional Reaction-Diffusion Equations Driven by Superlinear Multiplicative Noise on R^n |
| topic | Probability Analysis of PDEs 60F10, 60H15, 37L55, 35R60 |
| url | https://arxiv.org/abs/2406.08722 |