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

Ryo Kobayashi; Shuichi Kawashima

doi:10.1619/fesi.51.371

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

Ryo Kobayashi^*, Shuichi Kawashima

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 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 L^p decay estimate of solutions by applying the time weighted L^p 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 L^p -L^q decay estimate for the linearized problem.

Original language	English
Pages (from-to)	371-394
Number of pages	24
Journal	Funkcialaj Ekvacioj
Volume	51
Issue number	3
DOIs	https://doi.org/10.1619/fesi.51.371
Publication status	Published - 2008
Externally published	Yes

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

Access to Document

10.1619/fesi.51.371

Cite this

@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",

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

Y1 - 2008

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

SN - 0532-8721

VL - 51

SP - 371

EP - 394

JO - Funkcialaj Ekvacioj

JF - Funkcialaj Ekvacioj

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this