Asymptotic expansion of solutions to the drift-diffusion equation with large initial data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:369

Article

Yamamoto, Masakazu

关键词: Drift-diffusion equation;    Keller-Segel equation;    Asymptotic behavior of the solutions;   

DOI  :  10.1016/j.jmaa.2010.02.049

来源: Elsevier

【 摘 要 】

We consider the large-time behavior of the solution to the initial value problem for the Nernst-Planck type drift-diffusion equation in whole spaces. In the L(p)-framework, the global existence and the decay of the solution were shown. Moreover, the second-order asymptotic expansion of the solution as t -> infinity was derived. We also deduce the higher-order asymptotic expansion of the solution. Especially, we discuss the contrast between the odd-dimensional case and the even-dimensional case. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free