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

摘要

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-infinity well-posed. Moreover, we will apply such a result to the estimate of the existence time of the solution for Kirchhoff equation. Copyright (C) 2003 John Wiley Sons, Ltd. [References: 21]