A variational approach to stochastic nonlinear diffusion problems with dynamical boundary conditions

被引：4

作者：

Bonaccorsi, Stefano ^{[1
]}

Ziglio, Giacomo ^{[1
]}

机构：

[1] Univ Trento, Dipartimento Matemat, I-38123 Povo, Trento, Italy

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2014年 / 86卷 / 02期

关键词：

invariant measures; ergodicity; nonlinear operators; dynamical boundary conditions; PARTIAL-DIFFERENTIAL-EQUATIONS; ERGODICITY;

D O I：

10.1080/17442508.2013.775284

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise; we allow stochastic boundary conditions that depend on the time derivative of the solution on the boundary. This work provides the existence and uniqueness of the solution and it shows the existence of an ergodic invariant measure for the corresponding transition semigroup; furthermore, under suitable additional assumptions, uniqueness and strong asymptotic stability of the invariant measure are proved.

引用

页码：218 / 233

页数：16

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