Pathwise mild solutions for superlinear stochastic evolution equations and their attractors
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917910202548224 |
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| author | Blessing, Alexandra Seitz, Tim Sonner, Stefanie Tang, Bao Quoc |
| author_facet | Blessing, Alexandra Seitz, Tim Sonner, Stefanie Tang, Bao Quoc |
| contents | We investigate stochastic parabolic evolution equations with time-dependent random generators and locally Lipschitz continuous drift terms. Using pathwise mild solutions, we construct an infinite-dimensional stationary Ornstein-Uhlenbeck type process, which is shown to be tempered in suitable function spaces. This property, together with a bootstrapping argument based on the regularizing effect of parabolic evolution families, is then applied to prove the global well-posedness and the existence of a random attractor for reaction-diffusion equations with random non-autonomous generators and nonlinearities satisfying certain growth and dissipativity assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pathwise mild solutions for superlinear stochastic evolution equations and their attractors Blessing, Alexandra Seitz, Tim Sonner, Stefanie Tang, Bao Quoc Probability Analysis of PDEs Dynamical Systems We investigate stochastic parabolic evolution equations with time-dependent random generators and locally Lipschitz continuous drift terms. Using pathwise mild solutions, we construct an infinite-dimensional stationary Ornstein-Uhlenbeck type process, which is shown to be tempered in suitable function spaces. This property, together with a bootstrapping argument based on the regularizing effect of parabolic evolution families, is then applied to prove the global well-posedness and the existence of a random attractor for reaction-diffusion equations with random non-autonomous generators and nonlinearities satisfying certain growth and dissipativity assumptions. |
| title | Pathwise mild solutions for superlinear stochastic evolution equations and their attractors |
| topic | Probability Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2502.01209 |