A global existence and uniqueness result for a stochastic Allen–Cahn equation with constraint | Zendy

Bauzet C. | Zendy; Bonetti E. | Zendy; Bonfanti G. | Zendy; Lebon F. | Zendy; Vallet G. | Zendy

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

Author(s) -

Bauzet C.,

Bonetti E.,

Bonfanti G.,

Lebon F.,

Vallet G.

Publication year - 2017

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4383

Subject(s) - uniqueness , allen–cahn equation , discretization , constraint (computer aided design) , mathematics , monotone polygon , nonlinear system , operator (biology) , monotonic function , mathematical analysis , mathematical economics , physics , biochemistry , chemistry , geometry , repressor , quantum mechanics , transcription factor , gene

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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