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http://hdl.handle.net/10397/98873
Title: | Wellposedness and regularity estimates for stochastic Cahn–Hilliard equation with unbounded noise diffusion | Authors: | Cui, J Hong, J |
Issue Date: | Dec-2023 | Source: | Stochastic partial differential equations: analysis and computations, Dec. 2023, v. 11, no. 4, p. 1635-1671 | Abstract: | In this article, we consider the one dimensional stochastic Cahn–Hilliard equation driven by multiplicative space-time white noise with diffusion coefficient of sublinear growth. By introducing the spectral Galerkin method, we obtain the well-posedness of the approximated equation in finite dimension. Then with help of the semigroup theory and the factorization method, the approximation processes are shown to possess many desirable properties. Further, we show that the approximation process is strongly convergent in a certain Banach space with an explicit algebraic convergence rate. Finally, the global existence and regularity estimates of the unique solution process are proven by means of the strong convergence of the approximation process, which fills a gap on the global existence of the mild solution for stochastic Cahn–Hilliard equation when the diffusion coefficient satisfies a growth condition of order α∈(13,1). | Keywords: | Global existence Regularity estimate Spectral Galerkin method Stochastic Cahn–Hilliard equation Unbounded noise diffusion |
Publisher: | Springer | Journal: | Stochastic partial differential equations: analysis and computations | ISSN: | 2194-0401 | EISSN: | 2194-041X | DOI: | 10.1007/s40072-022-00272-8 | Rights: | © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s40072-022-00272-8. |
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