×

Large-time behavior of solutions to the drift-diffusion equation with fractional dissipation. (English) Zbl 1265.35131

Summary: 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 \(t\rightarrow \infty \) was obtained in the previous paper [M. Yamamoto, J. Math. Anal. Appl. 369, No. 1, 144–163 (2010; Zbl 1201.35050)]. We also derive the asymptotic expansion of the solution to the drift-diffusion equation with the fractional Laplacian.

MSC:

35K45 Initial value problems for second-order parabolic systems
35K58 Semilinear parabolic equations
35Q60 PDEs in connection with optics and electromagnetic theory
35B40 Asymptotic behavior of solutions to PDEs

Citations:

Zbl 1201.35050
PDFBibTeX XMLCite