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

J.L. Fischer, G. Grün, SIAM Journal on Mathematical Analysis 47 (2015) 825–854.

Download
No fulltext has been uploaded. References only!

Journal Article | Published
Author
;
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.
Publishing Year
Date Published
2015-01-01
Journal Title
SIAM Journal on Mathematical Analysis
Acknowledgement
The first author has been supported by the Lithuanian-Swiss co- operation program under the project agreement No. CH-SMM-01/0.
Volume
47
Issue
1
Page
825 - 854
IST-REx-ID

Cite this

Fischer JL, Grün G. Finite speed of propagation and waiting times for the stochastic porous medium equation: A unifying approach. SIAM Journal on Mathematical Analysis. 2015;47(1):825-854. doi:10.1137/140960578
Fischer, J. L., & Grün, G. (2015). Finite speed of propagation and waiting times for the stochastic porous medium equation: A unifying approach. SIAM Journal on Mathematical Analysis, 47(1), 825–854. https://doi.org/10.1137/140960578
Fischer, Julian L, and Günther Grün. “Finite Speed of Propagation and Waiting Times for the Stochastic Porous Medium Equation: A Unifying Approach.” SIAM Journal on Mathematical Analysis 47, no. 1 (2015): 825–54. https://doi.org/10.1137/140960578.
J. L. Fischer and G. Grün, “Finite speed of propagation and waiting times for the stochastic porous medium equation: A unifying approach,” SIAM Journal on Mathematical Analysis, vol. 47, no. 1, pp. 825–854, 2015.
Fischer JL, Grün G. 2015. Finite speed of propagation and waiting times for the stochastic porous medium equation: A unifying approach. SIAM Journal on Mathematical Analysis. 47(1), 825–854.
Fischer, Julian L., and Günther Grün. “Finite Speed of Propagation and Waiting Times for the Stochastic Porous Medium Equation: A Unifying Approach.” SIAM Journal on Mathematical Analysis, vol. 47, no. 1, Society for Industrial and Applied Mathematics , 2015, pp. 825–54, doi:10.1137/140960578.

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar