Non-existence of positive stationary solutions for a class of semi-linear PDE's with random coefficients
Résumé
We consider a so-called random obstacle model for the mo- tion 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 so- lution, 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 do- mains with Dirichlet boundary conditions. Difficulties arise because the
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