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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Cauchy problem for $ p$-evolution equations


Authors: Massimo Cicognani and Ferruccio Colombini
Journal: Trans. Amer. Math. Soc. 362 (2010), 4853-4869
MSC (2010): Primary 35G10, 35L15
Published electronically: April 28, 2010
MathSciNet review: 2645053
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Abstract: In this paper we deal with the Cauchy problem for evolution equations with real characteristics. We show that the problem is well-posed in Sobolev spaces assuming a suitable decay of the coefficients as the space variable $ x\to\infty$. In some cases, such a decay may also compensate a lack of regularity with respect to the time variable $ t$.


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Additional Information

Massimo Cicognani
Affiliation: Facoltà di Ingegneria II, Via Genova, 181, 47023 Cesena, Italy
Address at time of publication: Dipartimento di Matematica, Piazza di Porta S. Donato, 5, 40127 Bologna, Italy
Email: cicognani@dm.unibo.it

Ferruccio Colombini
Affiliation: Dipartimento di Matematica, University of Pisa, Largo Bruno Pontecorvo, 5, 56127 Pisa, Italy
Email: colombini@dm.unipi.it

DOI: http://dx.doi.org/10.1090/S0002-9947-10-05171-8
PII: S 0002-9947(10)05171-8
Keywords: Evolution equations with real characteristics
Received by editor(s): February 17, 2009
Published electronically: April 28, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.