Remark on Asymptotic Behaviors of Solutions to Quasi-Linear Elliptic Dirichlet Problem with Large Diffusion

Chunshan Zhao

doi:10.1016/j.na.2008.08.019

Remark on Asymptotic Behaviors of Solutions to Quasi-Linear Elliptic Dirichlet Problem with Large Diffusion

Chunshan Zhao

Mathematical Sciences

Georgia Southern University

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

1 Scopus citations

Abstract

We study asymptotic behaviors of nontrivial solutions to the Dirichlet problem of a quasi-linear elliptic equation and obtain a lower bound for growth of L^∞-norm of the solutions, which implies the L^∞-norm of the solutions goes to infinity as the diffusion coefficient goes to infinity.

Original language	American English
Journal	Nonlinear Analysis: Theory, Methods & Applications
Volume	70
DOIs	https://doi.org/10.1016/j.na.2008.08.019
State	Published - Jun 15 2009

Keywords

Asymptotic behavior
Dirichlet problem
Quasi-linear elliptic equation
m-Laplace operator

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title = "Remark on Asymptotic Behaviors of Solutions to Quasi-Linear Elliptic Dirichlet Problem with Large Diffusion",

abstract = "We study asymptotic behaviors of nontrivial solutions to the Dirichlet problem of a quasi-linear elliptic equation and obtain a lower bound for growth of L∞-norm of the solutions, which implies the L∞-norm of the solutions goes to infinity as the diffusion coefficient goes to infinity.",

keywords = "Asymptotic behavior, Dirichlet problem, Quasi-linear elliptic equation, m-Laplace operator",

author = "Chunshan Zhao",

year = "2009",

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language = "American English",

volume = "70",

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T1 - Remark on Asymptotic Behaviors of Solutions to Quasi-Linear Elliptic Dirichlet Problem with Large Diffusion

AU - Zhao, Chunshan

PY - 2009/6/15

Y1 - 2009/6/15

N2 - We study asymptotic behaviors of nontrivial solutions to the Dirichlet problem of a quasi-linear elliptic equation and obtain a lower bound for growth of L∞-norm of the solutions, which implies the L∞-norm of the solutions goes to infinity as the diffusion coefficient goes to infinity.

AB - We study asymptotic behaviors of nontrivial solutions to the Dirichlet problem of a quasi-linear elliptic equation and obtain a lower bound for growth of L∞-norm of the solutions, which implies the L∞-norm of the solutions goes to infinity as the diffusion coefficient goes to infinity.

KW - Asymptotic behavior

KW - Dirichlet problem

KW - Quasi-linear elliptic equation

KW - m-Laplace operator

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/248

UR - https://doi.org/10.1016/j.na.2008.08.019

U2 - 10.1016/j.na.2008.08.019

DO - 10.1016/j.na.2008.08.019

M3 - Article

VL - 70

JO - Nonlinear Analysis: Theory, Methods & Applications

JF - Nonlinear Analysis: Theory, Methods & Applications

ER -

Remark on Asymptotic Behaviors of Solutions to Quasi-Linear Elliptic Dirichlet Problem with Large Diffusion

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