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.
A global existence and uniqueness result for a stochastic Allen-Cahn equation with constraint / C. Bauzet, E. Bonetti, G. Bonfanti, F. Lebon, G. Vallet. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - 40:14(2017), pp. 5241-5261. [10.1002/mma.4383]
A global existence and uniqueness result for a stochastic Allen-Cahn equation with constraint
E. Bonetti;
2017
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.File | Dimensione | Formato | |
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