A global existence and uniqueness result for a stochastic Allen–Cahn equation with constraint - Archive ouverte HAL Accéder directement au contenu
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

C. Bauzet
  • Fonction : Auteur
E. Bonetti
  • Fonction : Auteur
G. Bonfanti

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. Copyright © 2017 John Wiley & Sons, Ltd.

Dates et versions

hal-04312919 , version 1 (28-11-2023)

Identifiants

Citer

C. Bauzet, E. Bonetti, G. Bonfanti, F. 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-04312919⟩
8 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More