Publications in Scientific Journals:
F. Achleitner, A. Jüngel, M. Yamamoto:
"Large-time asymptotics of a fractional drift-diffusion-Poisson system via the entropy method.";
Nonlinear Analysis: Theory, Methods and Applications,
179
(2019),
270
- 293.
English abstract:
The self-similar asymptotics for solutions to the drift-diffusion equation with fractional dissipation, coupled to the Poisson equation, is analyzed in the whole space. It is shown that in the subcritical and supercritical cases, the solutions converge to the fractional heat kernel with algebraic rate. The proof is based on the entropy method and leads to a decay rate in the L^1(R^d) norm. The technique is applied to other semilinear equations with fractional dissipation.
Keywords:
Drift-diffusion-Poisson system, Fractional dissipation, Self-similar asymptotics, Large-time behavior
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.na.2018.08.017
Created from the Publication Database of the Vienna University of Technology.