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July/August 2012 Large-time behavior of solutions to the drift-diffusion equation with fractional dissipation
Masakazu Yamamoto
Differential Integral Equations 25(7/8): 731-758 (July/August 2012).

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.

Citation

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Masakazu Yamamoto. "Large-time behavior of solutions to the drift-diffusion equation with fractional dissipation." Differential Integral Equations 25 (7/8) 731 - 758, July/August 2012.

Information

Published: July/August 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1265.35131
MathSciNet: MR2975693

Subjects:
Primary: 35B40, 35K45, 35K55, 35Q60, 78A35

Rights: Copyright © 2012 Khayyam Publishing, Inc.

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Vol.25 • No. 7/8 • July/August 2012
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