随机一般多孔介质与快速扩散方程(英文)

On stochastic generalized porous media and fast-diffusion equations

基于作者和合作者的有关工作,本文介绍关于随机一般多孔介质与快速扩散方程研究的若干新进展。我们从确定性的方程出发,引入相应随机方程的一般框架,再分别介绍解的存在唯一性、Harnack不等式与应用、解的正则性和大偏差原理等。

In terms of some recent work of the author and collaborators,this paper provides a self-contained account for the study of stochastic generalized porous media and fast-diffusion equations.We start from the corresponding deterministic equations in PDEs to explain the framework of the study,then introduce,respectively,results on the existence and uniqueness of solutions,the Harnack inequality for the associated transition semigroups and applications,the L2-solutions and Large deviation principles with small noise.