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Loss of regularity for the solutions to hyperbolic equations with non-regular coefficients—an application to Kirchhoff equation

✍ Scribed by Fumihiko Hirosawa

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
148 KB
Volume
26
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider the Cauchy problem for second‐order strictly hyperbolic equations with time‐depending non‐regular coefficients. There is a possibility that singular coefficients make a regularity loss for the solution. The main purpose of this paper is to derive an optimal singularity for the coefficient that the Cauchy problem is C^∞^ well‐posed. Moreover, we will apply such a result to the estimate of the existence time of the solution for Kirchhoff equation. Copyright © 2003 John Wiley & Sons, Ltd.

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