Research

Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients


Reference:

Coville, J., Dirr, N. and Luckhaus, S., 2010. Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients. Networks and Heterogeneous Media, 5 (4), pp. 745-763.

Related documents:

This repository does not currently have the full-text of this item.
You may be able to access a copy if URLs are provided below. (Contact Author)

Official URL:

http://dx.doi.org/10.3934/nhm.2010.5.745

Abstract

We consider a so-called random obstacle model for the motion of a hypersurface through a field of random obstacles, driven by a constant driving field. The resulting semi-linear parabolic PDE with random coefficients does not admit a global nonnegative stationary solution, which implies that an interface that was flat originally cannot get stationary. The absence of global stationary solutions is shown by proving lower bounds on the growth of stationary solutions on large domains with Dirichlet boundary conditions. Difficulties arise because the random lower order part of the equation cannot be bounded uniformly.

Details

Item Type Articles
CreatorsCoville, J., Dirr, N. and Luckhaus, S.
DOI10.3934/nhm.2010.5.745
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code22151

Export

Actions (login required)

View Item