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arXiv 0801.24782008-01-16math.PRmath-phmath.APmath.MP

随机多孔介质方程与自组织临界性

Stochastic Porous Media Equation and Self-Organized Criticality

Viorel Barbu, Giuseppe Da Prato, Michael Röckner

备注：: 29 pages, BiBoS-Preprint No. 07-11-268
发表信息：: Ann. Probab. 37 (2009), no. 2, 428-452
DOI：: 10.1007/s00220-008-0651-x

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摘要：

证明了具有非强制单调扩散函数和Wiener强迫项的随机多孔介质方程非负强解的存在唯一性。在1-D中证明了高概率解的有限时间灭绝性。所得结果与具有临界状态的随机非线性扩散方程的自组织临界行为有关。

英文摘要：

The existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and Wiener forcing term is proven. The finite time extinction of solutions with high probability is also proven in 1-D. The results are relevant for self-organized critical behaviour of stochastic nonlinear diffusion equations with critical states.

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