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

作者：Yamamoto Masakazu^*

来源：Journal of Mathematical Analysis and Applications, 2010, 369(1): 144-163.

DOI：10.1016/j.jmaa.2010.02.049

• Drift-diffusion equation
• Keller-Segel equation
• Asymptotic behavior of the solutions

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.

• 出版日期2010-9-1