Finite speed of propagation and waiting times for the stochastic porous medium equation: A unifying approach Journal Article


Author(s): Fischer, Julian; Grün, Günther
Article Title: Finite speed of propagation and waiting times for the stochastic porous medium equation: A unifying approach
Affiliation
Abstract: In this paper, we develop an energy method to study finite speed of propagation and waiting time phenomena for the stochastic porous media equation with linear multiplicative noise in up to three spatial dimensions. Based on a novel iteration technique and on stochastic counterparts of weighted integral estimates used in the deterministic setting, we formulate a sufficient criterion on the growth of initial data which locally guarantees a waiting time phenomenon to occur almost surely. Up to a logarithmic factor, this criterion coincides with the optimal criterion known from the deterministic setting. Our technique can be modified to prove finite speed of propagation as well.
Keywords: Waiting time; Finite propagation; Qualitative behavior; Stochastic partial differential equation; Stochastic porous medium equation
Journal Title: SIAM Journal on Mathematical Analysis
Volume: 47
Issue 1
ISSN: 1095-7154
Publisher: Society for Industrial and Applied Mathematics  
Date Published: 2015-01-01
Start Page: 825
End Page: 854
Sponsor: The first author has been supported by the Lithuanian-Swiss co- operation program under the project agreement No. CH-SMM-01/0.
DOI: 10.1137/140960578
Open access: no
IST Austria Authors
  1. Julian Fischer
    13 Fischer