Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2019

The Neumann problem for a Barenblatt equation with a multiplicative stochastic force and a nonlinear source term

Résumé

In this paper, we are interested in an existence and uniqueness result for a Barenblatt's type equation forced by a multiplicative noise, with additionally a nonlinear source term and under Neumann boundary conditions. The idea to show such a well-posedness result is to investigate in a first step the additive case with a linear source term. Trough a time-discretization of the equation and thanks to results on maximal monotone operator, one is able to handle the non-linearity of the equation and pass to the limit on the discretization parameter. This allows us to show existence and uniqueness of a solution in the case of an additive noise and a linear source term. In a second step, thanks to a fixed point procedure, one shows the announced result.

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hal-01910747 , version 1 (01-11-2018)

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Caroline Bauzet, Frédéric Lebon, Asghar Maitlo. The Neumann problem for a Barenblatt equation with a multiplicative stochastic force and a nonlinear source term. Nonlinear Differential Equations and Applications, 2019, ⟨10.1007/s00030-019-0567-5⟩. ⟨hal-01910747⟩
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