Global existence and gradient estimates for the quasilinear parabolic equations of m-Laplacian type with a nonlinear convection term

Mitsuhiro Nakao, Caisheng Chen

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

In this paper, we derive precise estimates for ∇u(t) including smoothing effects near t=0 and decay as t→∞ as well as global existence of the solutions u(t) to the initial-boundary value problem in a bounded domain in Rn for the quasilinear parabolic equation of the m Laplacian type with a nonlinear convection term b(u)∇u. For the initial data u0 we only assume u0∈Lq(Ω), 1≤q<∞.

Original languageEnglish
Pages (from-to)224-250
Number of pages27
JournalJournal of Differential Equations
Volume162
Issue number1
DOIs
Publication statusPublished - 2000 Mar 20
Externally publishedYes

Fingerprint

Smoothing Effect
Gradient Estimate
Quasilinear Parabolic Equations
Global Existence
Initial-boundary-value Problem
Boundary value problems
Convection
Bounded Domain
Decay
Term
Estimate

Keywords

  • Convection
  • Global existence
  • Gradient estimate
  • Quasilinear parabolic equation

ASJC Scopus subject areas

  • Analysis

Cite this

Global existence and gradient estimates for the quasilinear parabolic equations of m-Laplacian type with a nonlinear convection term. / Nakao, Mitsuhiro; Chen, Caisheng.

In: Journal of Differential Equations, Vol. 162, No. 1, 20.03.2000, p. 224-250.

Research output: Contribution to journalArticle

@article{923d0b2c8d4a485896e84c5c2054fff6,
title = "Global existence and gradient estimates for the quasilinear parabolic equations of m-Laplacian type with a nonlinear convection term",
abstract = "In this paper, we derive precise estimates for ∇u(t) including smoothing effects near t=0 and decay as t→∞ as well as global existence of the solutions u(t) to the initial-boundary value problem in a bounded domain in Rn for the quasilinear parabolic equation of the m Laplacian type with a nonlinear convection term b(u)∇u. For the initial data u0 we only assume u0∈Lq(Ω), 1≤q<∞.",
keywords = "Convection, Global existence, Gradient estimate, Quasilinear parabolic equation",
author = "Mitsuhiro Nakao and Caisheng Chen",
year = "2000",
month = "3",
day = "20",
doi = "10.1006/jdeq.1999.3694",
language = "English",
volume = "162",
pages = "224--250",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Global existence and gradient estimates for the quasilinear parabolic equations of m-Laplacian type with a nonlinear convection term

AU - Nakao, Mitsuhiro

AU - Chen, Caisheng

PY - 2000/3/20

Y1 - 2000/3/20

N2 - In this paper, we derive precise estimates for ∇u(t) including smoothing effects near t=0 and decay as t→∞ as well as global existence of the solutions u(t) to the initial-boundary value problem in a bounded domain in Rn for the quasilinear parabolic equation of the m Laplacian type with a nonlinear convection term b(u)∇u. For the initial data u0 we only assume u0∈Lq(Ω), 1≤q<∞.

AB - In this paper, we derive precise estimates for ∇u(t) including smoothing effects near t=0 and decay as t→∞ as well as global existence of the solutions u(t) to the initial-boundary value problem in a bounded domain in Rn for the quasilinear parabolic equation of the m Laplacian type with a nonlinear convection term b(u)∇u. For the initial data u0 we only assume u0∈Lq(Ω), 1≤q<∞.

KW - Convection

KW - Global existence

KW - Gradient estimate

KW - Quasilinear parabolic equation

UR - http://www.scopus.com/inward/record.url?scp=0034688720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034688720&partnerID=8YFLogxK

U2 - 10.1006/jdeq.1999.3694

DO - 10.1006/jdeq.1999.3694

M3 - Article

VL - 162

SP - 224

EP - 250

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -