On the nonlinear wave equation utt−B(t,‖u‖2,‖ux‖2) uxx=f(x,t,u,ux,ut,‖u‖2,‖ux‖2) associated with the mixed homogeneous conditions
In: Journal of Mathematical Analysis & Applications, Jg. 306 (2005-06-01), Heft 1, S. 243-268
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Abstract: In this paper we consider the following nonlinear wave equation: [(1)] , , , [(2)] , [(3)] , , where , are given constants and B, f, , are given functions. In Eq. (1), the nonlinear terms , depend on the integrals and . In this paper I associate with problem (1)–(3) a linear recursive scheme for which the existence of a local and unique solution is proved by using standard compactness argument. In case of , , , , and we obtain for the following equation associated to (2), (3) a weak solution having an asymptotic expansion of order in ɛ, for ɛ sufficiently small. [Copyright &y& Elsevier]
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On the nonlinear wave equation utt−B(t,‖u‖2,‖ux‖2) uxx=f(x,t,u,ux,ut,‖u‖2,‖ux‖2) associated with the mixed homogeneous conditions
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Autor/in / Beteiligte Person: | Long, Nguyen Thanh |
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Zeitschrift: | Journal of Mathematical Analysis & Applications, Jg. 306 (2005-06-01), Heft 1, S. 243-268 |
Veröffentlichung: | 2005 |
Medientyp: | academicJournal |
ISSN: | 0022-247X (print) |
DOI: | 10.1016/j.jmaa.2004.12.053 |
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