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...
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| Published in | Nonlinear analysis: real world applications Vol. 51; p. 102968 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.02.2020
Elsevier BV |
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| ISSN | 1468-1218 1878-5719 |
| DOI | 10.1016/j.nonrwa.2019.102968 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| ArticleNumber | 102968 |
| Author | Shang, Yadong Di, Huafei Song, Zefang |
| Author_xml | – sequence: 1 givenname: Huafei surname: Di fullname: Di, Huafei email: dihuafei@yeah.net organization: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, PR China – sequence: 2 givenname: Yadong surname: Shang fullname: Shang, Yadong email: gzydshang@126.com organization: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, PR China – sequence: 3 givenname: Zefang surname: Song fullname: Song, Zefang email: song_zefang@163.com organization: School of Economics and Statistics, Guangzhou University, Guangzhou 510006, PR China |
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| Keywords | Wave equation Logarithmic nonlinearity Strong damping Polynomial and exponential decay Finite time blow-up |
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| SubjectTerms | 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 |
| Title | Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity |
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