Author:
Cicognani Massimo,Hirosawa Fumihiko
Abstract
We consider the loss of regularity of the solution to the backward Cauchy problem for a second order strictly hyperbolic equation on the time interval $[0,T]$ with time depending coefficients which have a singularity only at the end point $t=0$. The main purpose of this paper is to show that the loss of regularity of the solution on the Gevrey scale can be described by the order of differentiability of the coefficients on $(0,T]$, the order of singularities of each derivatives as $t\to0$ and a stabilization condition of the amplitude of oscillations described by an integral on $(0,T)$. Moreover, we prove the optimality of the conditions for $C^\infty$ coefficients on $(0,T]$ by constructing a counterexample.
Publisher
Det Kgl. Bibliotek/Royal Danish Library
Cited by
6 articles.
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