An example of the Cauchy problem well posed in any Gevrey class |
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Authors: | Ferruccio Colombini Tatsuo Nishitani |
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Institution: | (1) Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italia;(2) Department of Mathematics, Osaka University, Machikaneyama 1-16, Toyonaka 560-0043, Osaka, Japan |
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Abstract: | We study the Cauchy problem for second order hyperbolic operators in the Gevrey classes where H(t,x) is given by the limit of a finite sum of functions such as a(t)b(x) with a(t) ≥ 0, b(x) ≥ 0. As a result, for any given positive integer N, we give an example H(t,x) which depends not only on t but also on x such that the Cauchy problem for P is well posed in the Gevrey class of order N. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35L10 35L15 35S10 |
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