FINITE SPEED OF PROPAGATION FOR STOCHASTIC POROUS MEDIA EQUATIONS

被引：12
|
作者：
Gess, Benjamin [1 ]
机构：
[1] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2013年 / 45卷 / 05期
关键词：
stochastic partial differential equations; stochastic porous medium equation; finite speed of propagation; hole-filling; free boundary; RANDOM ATTRACTORS; WEAK SOLUTIONS; EXISTENCE; UNIQUENESS;
D O I：
10.1137/120894713
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any continuous driving signal, thus including fractional Brownian motion for all Hurst parameters. The explicit estimates are then used to prove that the corresponding random attractor has infinite fractal dimension.
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页码：2734 / 2766
页数：33
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