arXiv math/07016062007-01-22math.APmath.FA

Dispersion and asymptotic profiles for Kirchhoff equations

Tokio Matsuyama, Michael Ruzhansky

发表信息：: in: Topics in contemporary differential geometry, complex analysis and mathematical physics. 234-243, World Sci. Publ., Hackensack, NJ, 2007.

英文摘要：

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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