Modulus of continuity of the coefficients and (non)quasianalytic solutions in the strictly hyperbolic Cauchy problem |
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Authors: | Massimo Cicognani Ferruccio Colombini |
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Institution: | a Facoltà di Ingegneria II, Via Genova, 181, 47023 Cesena, Italy b Dipartimento di Matematica, Piazza di Porta S. Donato, 5, 40127 Bologna, Italy c Dipartimento di Matematica, Largo Bruno Pontecorvo, 5, 56127 Pisa, Italy |
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Abstract: | In the strictly hyperbolic Cauchy problem, we investigate the relation between the modulus of continuity in the time variable of the coefficients and the well-posedness in Beurling-Roumieu classes of ultradifferentiable functions and functionals. We find well-posedness in nonquasianalytic classes assuming that the coefficients have modulus of continuity tω(1/t) such that . This condition is sharp because, in the case , we provide examples of Cauchy problems which are well-posed only in quasianalytic classes. |
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Keywords: | Cauchy problem Regularity of coefficients (Non)quasianalytic solutions |
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