Large time behavior of solutions to semilinear systems of wave equations |
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| Authors: | Hideo Kubo Kôji Kubota Hideaki Sunagawa |
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| Institution: | (1) Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka Osaka, 560-0043, Japan;(2) Atsubetsu Sapporo, 004-0001, Japan;(3) Institute of Mathematics, University of Tsukuba, Tsukuba Ibaraki, 305-8571, Japan |
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| Abstract: | This paper is concerned with the initial value problem for semilinear systems of wave equations. First we show a global existence
result for small amplitude solutions to the systems. Then we study asymptotic behavior of the global solution. We underline
that ``modified' free profiles are obtained for all global solutions to the systems even in the case where the free profile
might not exist. Moreover, we prove non–existence of any free profiles for the global solution in some cases where the effect
of the nonlinearity is strong enough.
The first author was partially supported by Grant-in-Aid for Science Research (14740114), JSPS. |
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| Keywords: | semilinear wave equations large time behavior radially symmetric solution |
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