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The Cauchy problem for  -evolution equations
Author(s):
Massimo
Cicognani;
Ferruccio
Colombini
Journal:
Trans. Amer. Math. Soc.
362
(2010),
4853-4869.
MSC (2010):
Primary 35G10, 35L15
Posted:
April 28, 2010
MathSciNet review:
2645053
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Additional information
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  . In some cases, such a decay may also compensate a lack of regularity with respect to the time variable  .
References:
-
- 1.
- Cicognani, M.; Colombini, F.: Sharp regularity of the coefficients in the Cauchy Problem for a class of evolution equations. Differential and Integral Equations 16 (2003), 1321-1344. MR 2016685 (2005a:35045)
- 2.
- Cicognani, M.; Colombini, F.: Loss of Derivatives in Evolution Cauchy Problems. Ann. Univ. Ferrara 52 (2006), 271-280 (in memoria di Stefano Benvenuti). MR 2273098 (2008f:35039)
- 3.
- Colombini, F.; De Giorgi, E.; Spagnolo, S.: Sur les équations hyperboliques avec des coefficients qui ne dependent que du temps. Ann. Sc. Norm. Sup. Pisa 6 (1979), 511-559. MR 553796 (81c:35077)
- 4.
- Colombini, F.; Lerner, N.: Hyperbolic operators with non-Lipschitz coefficients. Duke Math. J. 77 (1995), 657-698. MR 1324638 (96d:35075)
- 5.
- Colombini, F.; Métivier, G.: The Cauchy Problem for Wave Equations with non Lipschitz Coefficients; Application to continuation of solutions of some nonlinear wave equations. Ann. Sci. École Norm. Sup. 41 (2008), 177-220. MR 2468481 (2009k:35194)
- 6.
- Ichinose, W.: Some remarks on the Cauchy problem for Schrödinger type equations. Osaka J. Math. 21 (1984), 565-581. MR 759481 (86f:35060)
- 7.
- Kajitani, K.; Baba, A.: The Cauchy problem for Schrödinger type equations. Bull. Sci. Math. 119 (1995), 459-473. MR 1354247 (96m:35060)
- 8.
- Kumano-Go, H.: Pseudo-differential operators. The MIT Press, Cambridge, London, 1982.
- 9.
- Mizohata, S.: On the Cauchy problem. Academic Press, Orlando, FL; Science Press, Beijing, 1985. MR 860041 (89a:35007)
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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:
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
Posted:
April 28, 2010
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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