Well-posedness and large deviations of fractional McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917695132270592 |
|---|---|
| author | Chen, Zhang Wang, Bixiang |
| author_facet | Chen, Zhang Wang, Bixiang |
| contents | This paper is mainly concerned with the large deviation principle of the fractional McKean-Vlasov stochastic reaction-diffusion equation defined on R^n with polynomial drift of any degree. We first prove the well-posedness of the underlying equation under a dissipative condition, and then show the strong convergence of solutions of the corresponding controlled equation with respect to the weak topology of controls, by employing the idea of uniform tail-ends estimates of solutions in order to circumvent the non-compactness of Sobolev embeddings on unbounded domains. We finally establish the large deviation principle of the fractional McKean-Vlasov equation by the weak convergence method without assuming the time Holder continuity of the non-autonomous diffusion coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness and large deviations of fractional McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains Chen, Zhang Wang, Bixiang Probability Analysis of PDEs 60F10, 60H15, 37L55, 35R60 This paper is mainly concerned with the large deviation principle of the fractional McKean-Vlasov stochastic reaction-diffusion equation defined on R^n with polynomial drift of any degree. We first prove the well-posedness of the underlying equation under a dissipative condition, and then show the strong convergence of solutions of the corresponding controlled equation with respect to the weak topology of controls, by employing the idea of uniform tail-ends estimates of solutions in order to circumvent the non-compactness of Sobolev embeddings on unbounded domains. We finally establish the large deviation principle of the fractional McKean-Vlasov equation by the weak convergence method without assuming the time Holder continuity of the non-autonomous diffusion coefficients. |
| title | Well-posedness and large deviations of fractional McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains |
| topic | Probability Analysis of PDEs 60F10, 60H15, 37L55, 35R60 |
| url | https://arxiv.org/abs/2406.10694 |