论文信息 - Weak solutions to stochastic porous media equations

Weak solutions to stochastic porous media equations

Abstract A stochastic version of the porous medium equation is studied. The corresponding Kolmogorov equation is solved in a space $L^{2}(H, \nu)$ where ν is an invariant measure. Then a weak solution, that is a solution in the sense of the corresponding martingale problem, is constructed.

Michael Röckner | M. Röckner | Giuseppe Da Prato | G. Da Prato

[1] Wilhelm Stannat,et al. The theory of generalized Dirichlet forms and its applications in analysis and stochastics , 1999 .

[2] D. W. Stroock,et al. Multidimensional Diffusion Processes , 1979 .

[3] G. Prato,et al. Singular dissipative stochastic equations in Hilbert spaces , 2002 .

[4] M. Fukushima,et al. Dirichlet forms and symmetric Markov processes , 1994 .

[5] V. Bogachev,et al. Elliptic equations for measures on infinite dimensional spaces and applications , 2001 .

[6] A. Eberle. Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators , 2000 .

[7] Viorel Barbu,et al. Analysis and control of nonlinear infinite dimensional systems , 1993 .

[8] Michael Röckner,et al. Invariant Measures for a Stochastic Porous Medium Equation , 2004 .

[9] V. Barbu,et al. The two phase stochastic Stefan problem , 2002 .

[10] Zhi-Ming Ma,et al. Introduction to the theory of (non-symmetric) Dirichlet forms , 1992 .

[11] M. Röckner. L p -analysis of finite and infinite dimensional diffusion operators , 1999 .

[12] D. Aronson. The porous medium equation , 1986 .