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

J Coville, Nicolas Dirr, S Luckhaus

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)745-763
Number of pages19
JournalNetworks and Heterogeneous Media
Volume5
Issue number4
DOIs
Publication statusPublished - Nov 2010

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Random Coefficients
Stationary Solutions
Semilinear
Nonexistence
Boundary conditions
Parabolic PDEs
Dirichlet Boundary Conditions
Hypersurface
Non-negative
Lower bound
Imply
Motion
Class
Model

Cite this

Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients. / Coville, J; Dirr, Nicolas; Luckhaus, S.

In: Networks and Heterogeneous Media, Vol. 5, No. 4, 11.2010, p. 745-763.

Research output: Contribution to journalArticle

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