THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LÉVY JUMP

doi:10.1016/S0252-9602(11)60286-5

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 925-933.doi: 10.1016/S0252-9602(11)60286-5

THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LÉVY JUMP

周国立^1,2|侯振挺^1*

1. School of Mathematics, Central South University, Changsha 410075, China|

2. College of Mathematics and Statistis, Changqing University, Chongqing 401331, China

出版日期:2011-05-20 发布日期:2011-05-20
通讯作者: 侯振挺 E-mail:zhouguoli736@126.com; zthou@csu.edu.cn
基金资助:
The work was supported by the National Science Foundation of China (10671212; 90820302) and the National Science Foundation of Hunan Province.

THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LÉVY JUMP

ZHOU Guo-Li^1,2, HOU Zhen-Ting^1*

1. School of Mathematics, Central South University, Changsha 410075, China|

2. College of Mathematics and Statistis, Changqing University, Chongqing 401331, China

Online:2011-05-20 Published:2011-05-20
Contact: Hou Zhenting E-mail:zhouguoli736@126.com; zthou@csu.edu.cn
Supported by:
The work was supported by the National Science Foundation of China (10671212; 90820302) and the National Science Foundation of Hunan Province.

摘要/Abstract

摘要：

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 (p_t)_t≥0 to equilibrium uniform on any bounded subset in H.

关键词: stochastic porous medium equation, Lévy processes, ergodicity

Abstract:

Key words: stochastic porous medium equation, Lévy processes, ergodicity

中图分类号:

76S05

周国立, 侯振挺. THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LÉVY JUMP[J]. 数学物理学报(英文版), 2011, 31(3): 925-933.

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.

参考文献

[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

THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LÉVY JUMP

THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LÉVY JUMP

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