Large-time behavior of solutions to the drift-diffusion equation with fractional dissipation
2012
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.
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