The stochastic p-Laplace equation beyond the classical framework: Well-posedness, memory effects and approximations

我们考虑超越经典单调算子理论的随机p-Laplace发展方程。研究项目由三部分组成：-具有记忆效应的随机p-Laplace方程-具有对流-离散化和逼近的随机p-Laplace方程的理论方面。前两部分研究了具有对流和记忆效应的随机p-Laplace方程的适定性。第三部分对随机p-Laplace发展方程提出了关于时间变量的半隐式全离散格式和关于空间变量的有限体积型全离散格式，并研究了这些格式的收敛问题。该研究项目是在德法合作的框架内实施的，该合作由杰出的女数学家组成。

We consider stochastic p-Laplace evolution equations beyond the classical theory of monotone operators. The research project consists of three parts:- Stochastic p-Laplace equations with memory effects- Theoretical aspects of the stochastic p-Laplace equation with convection- Discretisation and approximations.The first two parts of the research project have a theoretical focus of the well-posedness of stochastic p-Laplace equations with convection and memory effects. In the third part, full discretisation schemes, semi-implicit with respect to the time variable and of finite-volume type with respect to the space variable, are proposed for stochastic p-Laplace evolution equations and the convergence of these schemes is investigated. The research project is implemented within the framework of a German-French cooperation of outstanding female mathematicians.