Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity

This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity utt−Δu−Δut=φp(u)log|u| in a bounded domain Ω⊂Rn. We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions und...

Full description

Saved in:
Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 51; p. 102968
Main Authors Di, Huafei, Shang, Yadong, Song, Zefang
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Ltd 01.02.2020
Elsevier BV
Subjects
Boundary value problems
Concavity
Finite time blow-up
Logarithmic nonlinearity
Mathematical analysis
Nonlinearity
Perturbation
Polynomial and exponential decay
Polynomials
Radon
Strong damping
Upper bounds
Wave equation
Wave equations
Wave equation
Logarithmic nonlinearity
Strong damping
Polynomial and exponential decay
Finite time blow-up
Online AccessGet full text
ISSN1468-1218
1878-5719
DOI10.1016/j.nonrwa.2019.102968

Cover

More Information
Summary:This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity utt−Δu−Δut=φp(u)log|u| in a bounded domain Ω⊂Rn. We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2019.102968