Decay estimates and large time behavior of solutions to the Drift-Diffusion system

Ryo Kobayashi, Shuichi Kawashima

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We study the drift-diffusion system arising in the semiconductor device simulation and the plasma physics. We consider the initial value problem for this system and derive the optimal Lp decay estimate of solutions by applying the time weighted Lp energy method. Furthermore, we show that the solutions approach the corresponding heat kernels as time tends to infinity. This asymptotic result is based on the optimal Lp -Lq decay estimate for the linearized problem.

Original languageEnglish
Pages (from-to)371-394
Number of pages24
JournalFunkcialaj Ekvacioj
Volume51
Issue number3
DOIs
Publication statusPublished - 2008 Dec 1
Externally publishedYes

Keywords

  • Decay estimate
  • Drift-diffusion system
  • L-L estimate
  • Large time behavior
  • Time weighted energy method

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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