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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2007, Volume 4, Pages 249–277
(Mi semr155)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/semr155 https://www.mathnet.ru/eng/semr/v4/p249
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