Asymptotic expansion of solutions to the drift-diffusion equation with large initial data
Asymptotic expansion of solutions to the drift-diffusion equation with large initial data
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DOI：
10.1016/j.jmaa.2010.02.049
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发表时间：
2010-09
影响因子：
1.3
通讯作者：
M. Yamamoto
中科院分区：
文献类型：
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作者：
M. Yamamoto
在全空间中考虑Nernst-Planck型漂移扩散方程初值问题解的大时间行为。在Lp-框架下，证明了解的整体存在性和衰减性.此外，还得到了当t→∞时解的二阶渐近展开式.我们还推导出了解的高阶渐近展开式。特别地，我们讨论了奇维情形和偶维情形的对比。
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 Lp-framework, the global existence and the decay of the solution were shown. Moreover, the second-order asymptotic expansion of the solution as t→∞ 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.