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Absolute Continuity of Solutions to Reaction-Diffusion Equations with Multiplicative Noise

Marinelli, C; Quer-Sardanyons, L; (2021) Absolute Continuity of Solutions to Reaction-Diffusion Equations with Multiplicative Noise. Potential Analysis , 54 (4) 10.1007/s11118-021-09914-3. Green open access

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Abstract

We prove absolute continuity of the law of the solution, evaluated at fixed points in time and space, to a parabolic dissipative stochastic PDE on L (G), where G is an open bounded domain in ℝ with smooth boundary. The equation is driven by a multiplicative Wiener noise and the nonlinear drift term is the superposition operator associated to a real function that is assumed to be monotone, locally Lipschitz continuous, and growing not faster than a polynomial. The proof, which uses arguments of the Malliavin calculus, crucially relies on the well-posedness theory in the mild sense for stochastic evolution equations in Banach spaces. 2 d

Type: Article
Title: Absolute Continuity of Solutions to Reaction-Diffusion Equations with Multiplicative Noise
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11118-021-09914-3
Publisher version: https://doi.org/10.1007/s11118-021-09914-3
Language: English
Additional information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Keywords: Stochastic PDEs, Reaction-diffusion equations, Malliavin calculus
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10125799
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