Dispersion and asymptotic profiles for Kirchhoff equations

Details Dispersion and asymptotic profiles for Kirchhoff equations Dispersion and asymptotic profiles for Kirchhoff equations

2007-01-22

arxiv.org/abs/math/0701606v1

in: Topics in contemporary differential geometry, complex analysis and mathematical physics. 234-243, World Sci. Publ., Hacken

Mathematics

Analysis of PDEs

Scientific paper

The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For this purpose, the method of asymptotic integration is developed for the corresponding linear equations and representation formulae for their solutions are obtained. These formulae are analysed further to obtain the time decay rate of $L^p$--$L^q$ norms of propagators for the corresponding Cauchy problems.

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