## Differential and Integral Equations

### Large-time behavior of solutions to the drift-diffusion equation with fractional dissipation

Masakazu Yamamoto

#### Abstract

We consider the Nernst-Planck-type drift-diffusion equation with fractional dissipation. For the initial-value problem of this equation, the well-posedness, the time-global existence, and the decay of solutions were already shown. When the dissipation operator is given by the Laplacian, the asymptotic expansion of the solution as $t\to\infty$ was obtained in a previous paper. We also derive the asymptotic expansion of the solution to the drift-diffusion equation with the fractional Laplacian.

#### Article information

Source
Differential Integral Equations, Volume 25, Number 7/8 (2012), 731-758.

Dates
First available in Project Euclid: 20 December 2012