Acta mathematica scientia, Series B >
THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LÉVY JUMP
Online published: 2011-05-20
Supported by
The work was supported by the National Science Foundation of China (10671212; 90820302) and the National Science Foundation of Hunan Province.
In this article, we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process, and then show the exponential convergence of (pt)t≥0 to equilibrium uniform on any bounded subset in H.
Key words： stochastic porous medium equation; Lévy processes; ergodicity
ZHOU Guo-Li , HOU Zhen-Ting . THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LÉVY JUMP[J]. Acta mathematica scientia, Series B, 2011 , 31(3) : 925 -933 . DOI: 10.1016/S0252-9602(11)60286-5
[1] Aronson D C. The porous medium equation//Farina A, Primicerio M, eds. Problems in Nonlinear Diffusion. Lecture Notes Math, Vol 1224. Berlin: Springer, 1986: 1--46
[2] Da Prato G, R\"{o}ckner M. Weak solutions to stochastic porus media equations. J Evol Equ, 2004, 4: 249--271
[3] Da Prato G, R\"{o}ckner M. Invariant measures for a stochastic Porus media equation//Kunita H, Takanashi Y, Watanabe S, eds. Stochastic Analysis and Related Topics. Advanced in Pure Math, 41. Japan Math Soc, 2004: 13--29
[4] Da Prato G, R\"{o}ckner M, Rozovskii B L, Wang F Y. Strong solutions of stochastic generalized porus media equations: Existence, uniqueness, and ergodicity. Commu Part Differ Equ, 2006, 31: 277--291
[5] Ebmeye C. Regularrity in Sobolev spaces for the fast diffusion and the porous medium equation. J Math Anal Appl, 2005, 307: 134--152
[6] Ren J, R\"{o}ckner M, Wang F Y. Stochastic generalized porous media and fast diffusion equation. J Differ Equ, 2007, 238(1): 118-152
[7] Kim J U. On the stochastic porous medium equation. J Diff Equ, 2006, 206: 163--94
[8] R\"{o}ckner M. Intruduction to stochastic partial differential equation. Purdue University, Fall 2005 and Spring 2006, Version: April 26, 2007
[9] R\"{o}ckner M, Wang F Y. Non-monotone stochastic generalized porous media equations.J Diff Equ, 2008, 245: 3898--3935
[10] Wang Fengyu. Harnack inequality and applications for stochastic generalized porous media equations. Ann Prob, 2007, 35(4): 1333--1350
[11] Yin Jinxue, Wang Liangwei, Huang Rui. Complexity of asymptotic behavior of solutions for the porous medium equation with absorption. Acta Math Sci, 2010, 30B(6): 1865--1880
[12] Zhou Guoli, Hou Zhengting. Stochastic generalized porous media equations with Lévy jump. Acta Mathematica Sinica, preprint
[13] Zhou Guoli, Hou Zhengting. The ergodicity of stochastic partial differential equations with Lévy jump. Acta Mathematica Sinica, preprint
/
| 〈 |
|
〉 |