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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2007, Volume 4, Pages 249–277 (Mi semr155)  

This article is cited in 3 scientific papers (total in 3 papers)

Research papers

Asymptotics for nonlinear damped wave equations with large initial data

N. Hayashia, E. I. Kaikinab, P. I. Naumkinb

a Department of Mathematics, Graduate School of Science, Osaka University, Japan
b Instituto de Matemáticas, Universidad Nacional Autónoma de México
Full-text PDF (842 kB) Citations (3)
References:
Abstract: We study the one dimensional nonlinear damped wave equation
\begin{equation} \begin{cases} u_{tt}+u_{t}-u_{xx}=\lambda|u|^{\sigma}u,&x\in\mathbf{R},\quad t>0,\\ u(0,x)=u_0(x),& x\in\mathbf{R},\\ u_t(0,x)=u_1(x),& x\in\mathbf{R}, \end{cases} \tag{0.1} \end{equation}
where $\sigma>0$, $\lambda\in\mathbf R$. Our aim is to prove the large time asymptotic formulas for solutions of the Cauchy problem (0.1) without any restriction on the size of the initial data.
Received August 25, 2006, published May 28, 2007
Bibliographic databases:
Document Type: Article
UDC: 517.955.8
MSC: 35Q40, 35B40
Language: English
Citation: N. Hayashi, E. I. Kaikina, P. I. Naumkin, “Asymptotics for nonlinear damped wave equations with large initial data”, Sib. Èlektron. Mat. Izv., 4 (2007), 249–277
Citation in format AMSBIB
\Bibitem{HayKaiNau07}
\by N.~Hayashi, E.~I.~Kaikina, P.~I.~Naumkin
\paper Asymptotics for nonlinear damped wave equations with large initial data
\jour Sib. \`Elektron. Mat. Izv.
\yr 2007
\vol 4
\pages 249--277
\mathnet{http://mi.mathnet.ru/semr155}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2465425}
\zmath{https://zbmath.org/?q=an:1132.35447}
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  • https://www.mathnet.ru/eng/semr/v4/p249
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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