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

Fingerprint

Drift-diffusion
Lp Estimates
Decay Estimates
Large Time Behavior
Behavior of Solutions
Semiconductor Device Simulation
Plasma Physics
Energy Method
Heat Kernel
Initial Value Problem
Infinity
Tend

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Decay estimates and large time behavior of solutions to the Drift-Diffusion system. / Kobayashi, Ryo; Kawashima, Shuichi.

In: Funkcialaj Ekvacioj, Vol. 51, No. 3, 01.12.2008, p. 371-394.

Research output: Contribution to journalArticle

@article{cdf74133dd2c4404b25a00514391bddf,
title = "Decay estimates and large time behavior of solutions to the Drift-Diffusion system",
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.",
keywords = "Decay estimate, Drift-diffusion system, L-L estimate, Large time behavior, Time weighted energy method",
author = "Ryo Kobayashi and Shuichi Kawashima",
year = "2008",
month = "12",
day = "1",
doi = "10.1619/fesi.51.371",
language = "English",
volume = "51",
pages = "371--394",
journal = "Funkcialaj Ekvacioj",
issn = "0532-8721",
publisher = "Mathematical Society of Japan - Kobe University",
number = "3",

}

TY - JOUR

T1 - Decay estimates and large time behavior of solutions to the Drift-Diffusion system

AU - Kobayashi, Ryo

AU - Kawashima, Shuichi

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

KW - Decay estimate

KW - Drift-diffusion system

KW - L-L estimate

KW - Large time behavior

KW - Time weighted energy method

UR - http://www.scopus.com/inward/record.url?scp=70450120341&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70450120341&partnerID=8YFLogxK

U2 - 10.1619/fesi.51.371

DO - 10.1619/fesi.51.371

M3 - Article

AN - SCOPUS:70450120341

VL - 51

SP - 371

EP - 394

JO - Funkcialaj Ekvacioj

JF - Funkcialaj Ekvacioj

SN - 0532-8721

IS - 3

ER -