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| Existence and Asymptotic Behavior of RadiallySymmetric Solutions to a Semilinear HyperbolicSystem in Odd Space Dimensions |
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Citation： |
Hideo KUBO,Koji KUBOTA.Existence and Asymptotic Behavior of RadiallySymmetric Solutions to a Semilinear HyperbolicSystem in Odd Space Dimensions[J].Chinese Annals of Mathematics B,2006,27(5):507~538 |
| Page view： 1121
Net amount： 961 |
Authors： |
Hideo KUBO; Koji KUBOTA |
Foundation： |
Project supported by Grant-in-Aid for Science Research (No.12740105, No.14204011), JSPS. |
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| Abstract： |
This paper is concerned with a class of semilinear hyperbolic
systems in odd space dimensions. Our main aim is to prove the
existence of a small amplitude solution which is asymptotic to
the free solution as $t \to -\infty$ in the energy norm, and to show it has a free profile as $t \to +\infty$.
Our approach is based on the work of \cite{kk1}. Namely we use a
weighted $L^\infty$ norm to get suitable a priori estimates. This
can be done by restricting our attention to radially symmetric
solutions. Corresponding initial value problem is also considered
in an analogous framework. Besides, we give an extended result of
\cite{kk4} for three space dimensional case in Section 5, which
is prepared independently of the other parts of the paper. |
Keywords： |
Semilinear wave equations, Asymptotic behavior, Radially symmetric
solution |
Classification： |
35L70 |
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