Stationary solutions for a model of amorphous thin-film growth

TL;DR

This paper studies a stochastic PDE model for amorphous thin film growth, demonstrating the existence of stationary solutions using spectral Galerkin methods, despite challenges in proving uniqueness and boundedness.

Contribution

It establishes the existence of stationary mild solutions for a class of stochastic PDEs modeling amorphous thin film growth, employing spectral Galerkin techniques.

Findings

Existence of stationary mild solutions verified

Spectral Galerkin method applied successfully

Uniqueness and boundedness remain unresolved

Abstract

We consider a class of stochastic partial differential equations arising as a model for amorphous thin film growth. Using a spectral Galerkin method, we verify the existence of stationary mild solutions, although the specific nature of the nonlinearity prevents us from showing the uniqueness of the solutions as well as their boundedness (in time).