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Article Dans Une Revue Mathematical Methods in the Applied Sciences Année : 2017

A global existence and uniqueness result for a stochastic Allen-Cahn equation with constraint

Résumé

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.
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hal-01694069 , version 1 (02-10-2018)

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Caroline Bauzet, Elena Bonetti, Giovanna Bonfanti, Frédéric Lebon, Guy Vallet. A global existence and uniqueness result for a stochastic Allen-Cahn equation with constraint. Mathematical Methods in the Applied Sciences, 2017, 40 (14), pp.5241-5261. ⟨10.1002/mma.4383⟩. ⟨hal-01694069⟩
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