Nonlinear stochastic evolution equations of second order with damping

TL;DR

This paper proves the convergence and existence of solutions for a fully discretized second order stochastic evolution equation with nonlinear damping, using an implicit scheme and internal approximation.

Contribution

It introduces a novel discretization scheme for second order stochastic equations with nonlinear damping and proves its convergence and uniqueness.

Findings

Convergence of the discretization scheme is established.

Existence and uniqueness of solutions are proved.

The scheme effectively approximates the stochastic evolution equation.

Abstract

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with an internal approximation. Uniqueness is proved as well.