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A global existence and uniqueness result for a stochastic Allen-Cahn equation with constraint
- Source :
- Mathematical Methods in the Applied Sciences. 40:5241-5261
- Publication Year :
- 2017
- Publisher :
- Wiley, 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.
- Subjects :
- Continuum (topology)
General Mathematics
010102 general mathematics
Mathematical analysis
General Engineering
Monotonic function
01 natural sciences
010101 applied mathematics
Constraint (information theory)
Nonlinear system
Character (mathematics)
Uniqueness
0101 mathematics
Allen–Cahn equation
Mathematics
Variable (mathematics)
Subjects
Details
- ISSN :
- 01704214
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........479e75ffbca040dc9d51c650bec45b95