Differential and Integral Equations

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

Masakazu Yamamoto

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012661

Mathematical Reviews number (MathSciNet)
MR2975693

Zentralblatt MATH identifier
1265.35131

Subjects
Primary: 35K45: Initial value problems for second-order parabolic systems 35K55: Nonlinear parabolic equations 35Q60: PDEs in connection with optics and electromagnetic theory 35B40: Asymptotic behavior of solutions 78A35: Motion of charged particles

Citation

Yamamoto, Masakazu. Large-time behavior of solutions to the drift-diffusion equation with fractional dissipation. Differential Integral Equations 25 (2012), no. 7/8, 731--758. https://projecteuclid.org/euclid.die/1356012661


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