A global existence and uniqueness result for a stochastic Allen–Cahn equation with constraint |
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| Authors: | C Bauzet E Bonetti G Bonfanti F Lebon G Vallet |
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| Affiliation: | 1. Aix‐Marseille University, CNRS, Centrale Marseille, Marseille, France;2. Department of Mathematics, University ofMilan, Milan, Italy;3. Department DICATAM – Section of Mathematics, University of Brescia, Brescia, Italy;4. Université de Pau et des Pays de l'Adour, LMAP, UMR CNRS 5142, IPRA, Pau, France |
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| Abstract: | This paper addresses the analysis of a time noise‐driven Allen–Cahn equation modelling the evolution of damage in continuum media in the presence of stochastic dynamics. The nonlinear character of the equation is mainly due to a multivoque maximal monotone operator representing a constraint on the damage variable, which is forced to take physically admissible values. By a Yosida approximation and a time‐discretization procedure, we prove a result of global‐in‐time existence and uniqueness of the solution to the stochastic problem. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | nonlinear parabolic equations stochastic PDEs existence and uniqueness |
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