Asymptotic behavior of solutions for a semilinear dissipative wave equations

Research output: Contribution to journalArticle

Abstract

We investigate asymptotic property of the solution to the boundary value problem (BV) for the semilinear Euler-Poisson-Darboux type equation as t tends to ∞. Applying this result to the boundary value problem of the semilinear wave equation with a nonlinear dissipation we show the optimality of the decay estimate. Also we discuss the optimality of the decay estimates and lower bounds of solutions the mixed problem corresponding to (BV).

Original languageEnglish
Pages (from-to)2527-2537
Number of pages11
JournalNonlinear Analysis, Theory, Methods and Applications
Volume47
Issue number4
DOIs
Publication statusPublished - 01-08-2001

Fingerprint

Dissipative Equations
Asymptotic Behavior of Solutions
Wave equations
Semilinear
Boundary value problems
Wave equation
Decay Estimates
Boundary Value Problem
Optimality
Nonlinear Dissipation
Semilinear Wave Equation
Mixed Problem
Asymptotic Properties
Euler
Siméon Denis Poisson
Tend
Lower bound

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

@article{703e621673064c84891eb5eae2356d6d,
title = "Asymptotic behavior of solutions for a semilinear dissipative wave equations",
abstract = "We investigate asymptotic property of the solution to the boundary value problem (BV) for the semilinear Euler-Poisson-Darboux type equation as t tends to ∞. Applying this result to the boundary value problem of the semilinear wave equation with a nonlinear dissipation we show the optimality of the decay estimate. Also we discuss the optimality of the decay estimates and lower bounds of solutions the mixed problem corresponding to (BV).",
author = "A. Kubo",
year = "2001",
month = "8",
day = "1",
doi = "10.1016/S0362-546X(01)00375-3",
language = "English",
volume = "47",
pages = "2527--2537",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",
number = "4",

}

Asymptotic behavior of solutions for a semilinear dissipative wave equations. / Kubo, A.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 47, No. 4, 01.08.2001, p. 2527-2537.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Asymptotic behavior of solutions for a semilinear dissipative wave equations

AU - Kubo, A.

PY - 2001/8/1

Y1 - 2001/8/1

N2 - We investigate asymptotic property of the solution to the boundary value problem (BV) for the semilinear Euler-Poisson-Darboux type equation as t tends to ∞. Applying this result to the boundary value problem of the semilinear wave equation with a nonlinear dissipation we show the optimality of the decay estimate. Also we discuss the optimality of the decay estimates and lower bounds of solutions the mixed problem corresponding to (BV).

AB - We investigate asymptotic property of the solution to the boundary value problem (BV) for the semilinear Euler-Poisson-Darboux type equation as t tends to ∞. Applying this result to the boundary value problem of the semilinear wave equation with a nonlinear dissipation we show the optimality of the decay estimate. Also we discuss the optimality of the decay estimates and lower bounds of solutions the mixed problem corresponding to (BV).

UR - http://www.scopus.com/inward/record.url?scp=0035422720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035422720&partnerID=8YFLogxK

U2 - 10.1016/S0362-546X(01)00375-3

DO - 10.1016/S0362-546X(01)00375-3

M3 - Article

AN - SCOPUS:0035422720

VL - 47

SP - 2527

EP - 2537

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 4

ER -