A global existence and uniqueness result for a stochastic Allen–Cahn equation with constraint. (29th March 2017)

• Record Type: Journal Article
• Authors: Bauzet, C.; Bonetti, E.; Bonfanti, G.; Lebon, F.; Vallet, G.
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 14(2017)
• Page Start: 5241
• Page End: 5261
• Publication Date: 2017-03-29
• Subjects: nonlinear parabolic equations -- stochastic PDEs -- existence and uniqueness; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4383
• Languages: English
• ISSNs: 0170-4214

Abstract

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.