Scarpa, L;
(2017)
Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type.
Journal of Differential Equations
, 263
(4)
pp. 2113-2156.
10.1016/j.jde.2017.03.041.
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Abstract
We prove well-posedness for doubly nonlinear parabolic stochastic partial differential equations of the form View the MathML source, where γ and β are the two nonlinearities, assumed to be multivalued maximal monotone operators everywhere defined on Rd and R respectively, and W is a cylindrical Wiener process. Using variational techniques, suitable uniform estimates (both pathwise and in expectation) and some compactness results, well-posedness is proved under the classical Leray–Lions conditions on γ and with no restrictive smoothness or growth assumptions on β. The operator B is assumed to be Hilbert–Schmidt and to satisfy some classical Lipschitz conditions in the second variable.
| Type: | Article |
|---|---|
| Title: | Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jde.2017.03.041 |
| Publisher version: | http://doi.org/10.1016/j.jde.2017.03.041 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Doubly nonlinear stochastic equation; Divergence; Variational approach; Existence of solutions; Continuous dependence; Multiplicative noise |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1547663 |
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