Piotr Biler, Jean Dolbeault
Long Time Behavior of Solutions to Nernst--Planck and Debye--H\\\
Preprint series: ESI preprints

MSC:

35Q99 None of the above but in this section

35B40 Asymptotic behavior of solutions

35B30 Dependence of solutions of PDE on initial and boundary data, parameters, See also {58F14}

Abstract: }We study the convergence rates of solutions to drift-diffusion
systems (arising from plasma, semiconductors and electrolytes theories) to their
self-similar or steady states. This analysis involves entropy-type Lyapunov
functionals and logarithmic Sobolev inequalities.
Keywords: drift-diffusion systems, asymptotic behavior of solutions, logarithmic Sobolev inequalities