Abstract

In this contribution, a stochastic nonlinear evolution system under Neumann boundary conditions is investigated. Precisely, we are interested in finding an existence and uniqueness result for a random heat equation coupled with a Barenblatt’s type equation with a multiplicative stochastic force in the sense of Itô. In a first step, we establish well-posedness in the case of an additive noise through a semi-implicit time discretization of the system. In a second step, the derivation of continuous dependence estimates of the solution with respect to the data allows us to show the desired existence and uniqueness result for the multiplicative case.

中文翻译：

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随机热方程与乘法随机 Barenblatt 方程耦合的适定性

摘要

在这个贡献中，研究了诺依曼边界条件下的随机非线性演化系统。准确地说，我们感兴趣的是找到随机热方程的存在性和唯一性结果，该方程与具有 Itô 意义上的乘法​​随机力的 Barenblatt 型方程相结合。第一步，我们通过系统的半隐式时间离散化在加性噪声的情况下建立适定性。在第二步中，解对数据的连续依赖估计的推导使我们能够显示乘法情况下所需的存在性和唯一性结果。