Stochastic Camassa-Holm equation with convection type noise
| Autor: | Alexei Daletskii, Sergio Albeverio, Zdzisław Brzeźniak |
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| Rok vydání: | 2021 |
| Předmět: |
Camassa–Holm equation
Partial differential equation Applied Mathematics 010102 general mathematics Operator theory Differential operator 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis 010101 applied mathematics Stochastic partial differential equation symbols.namesake Nonlinear system Mathematics - Analysis of PDEs Wiener process FOS: Mathematics symbols Applied mathematics Uniqueness 0101 mathematics Analysis Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Journal of Differential Equations. 276:404-432 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2020.12.013 |
| Popis: | We consider a stochastic Camassa-Holm equation driven by a one-dimensional Wiener process with a first order differential operator as diffusion coefficient. We prove the existence and uniqueness of local strong solutions of this equation. In order to do so, we transform it into a random quasi-linear partial differential equation and apply Kato's operator theory methods. Some of the results have potential to find applications to other nonlinear stochastic partial differential equations. |
| Databáze: | OpenAIRE |
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