| Abstract: |
| In this talk, I will present the proof of the existence and uniqueness of the solution of a stochastic phase-field problem modelling the melting of ice. I will consider a multiplicative noise induced by a Q-Brownian motion. The starting point is to perform a Galerkin approximation and establish a priori estimates for the solution pair of the corresponding approximate system. Since in the stochastic case the solutions are not differentiable in time and since we have an additional random variable, the usual compactness method used in the theory of deterministic nonlinear partial differential equations cannot be applied; therefore we use a stochastic compactness method based upon fractional Sobolev spaces. |
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