Asymptotic behavior of the stochastic Keller-Segel equations

Yadong Shang; Jianjun Paul Tian; Bixiang Wang

doi:10.3934/dcdsb.2019020

Article Contents

2019, Volume 24, Issue 3: 1367-1391. Doi: 10.3934/dcdsb.2019020

This issue Previous Article On the nonconserved Caginalp phase-field system based on the Maxwell-Cattaneo law with two temperatures and logarithmic potentials Next Article An optimal control problem for some nonlinear elliptic equations with unbounded coefficients

Asymptotic behavior of the stochastic Keller-Segel equations

1.
School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
2.
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88001, USA
3.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA

^* Corresponding author
^* Corresponding author

Received: December 2017

Revised: March 2018

Early access: January 2019

Published: January 2019

The second author was supported by NSF (DMS-1446139), NIH (U54CA132383) and NNSF of China (No.11371048).

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Abstract

This paper deals with the asymptotic behavior of the solutions of the non-autonomous one-dimensional stochastic Keller-Segel equations defined in a bounded interval with Neumann boundary conditions. We prove the existence and uniqueness of tempered pullback random attractors under certain conditions. We also establish the convergence of the solutions as well as the pullback random attractors of the stochastic equations as the intensity of noise approaches zero.

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Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 37L30.

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