RANDOM ATTRACTORS FOR STOCHASTIC POROUS MEDIA EQUATIONS PERTURBED BY SPACE-TIME LINEAR MULTIPLICATIVE NOISE

• 成果类型: Article
• 署名作者: Gess, Benjamin
• 署名单位: Humboldt University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP869
• 发表日期: 2014
• 页码: 818-864
• 关键词: partial-differential-equations; VISCOSITY SOLUTIONS; WEAK SOLUTIONS; EXISTENCE; uniqueness

摘要

Unique existence of solutions to porous media equations driven by continuous linear multiplicative space time rough signals is proven for initial data in L-1(O) on bounded domains O. The generation of a continuous, order-preserving random dynamical system on L-1(O) and the existence of a random attractor for stochastic porous media equations perturbed by linear multiplicative noise in space and time is obtained. The random attractor is shown to be compact and attracting in L-infinity(O) norm. Uniform L-infinity bounds and uniform space time continuity of the solutions is shown. General noise including fractional Brownian motion for all Hurst parameters is treated and a pathwise Wong-Zakai result for driving noise given by a continuous semi-martingale is obtained. For fast diffusion equations driven by continuous linear multiplicative space time rough signals, existence of solutions is proven for initial data in Lm+1(O).