Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Cauchy problem for a class of Kovalevskian pseudo-differential operators


Authors: Rossella Agliardi and Massimo Cicognani
Journal: Proc. Amer. Math. Soc. 132 (2004), 841-845
MSC (2000): Primary 35G10, 35L30
Published electronically: August 19, 2003
MathSciNet review: 2019963
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the $H^{\infty}$ well-posedness of the forward Cauchy problem for a pseudo-differential operator $P$ of order $m\geq 2$ with the Log-Lipschitz continuous symbol in the time variable. The characteristic roots $\lambda_k$ of $P$ are distinct and satisfy the necessary Lax-Mizohata condition Im $\lambda_k\geq 0$. The Log-Lipschitz regularity has been tested as the optimal one for $H^{\infty}$ well-posedness in the case of second-order hyperbolic operators. Our main aim is to present a simple proof which needs only a little of the basic calculus of standard pseudo-differential operators.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35G10, 35L30

Retrieve articles in all journals with MSC (2000): 35G10, 35L30


Additional Information

Rossella Agliardi
Affiliation: University of Ferrara, via Machiavelli 35, 44100 Ferrara, Italy
Email: agl@dns.unife.it

Massimo Cicognani
Affiliation: University of Bologna, via Genova 181, 47023 Cesena, Italy
Email: cicognan@dm.unibo.it

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07092-8
PII: S 0002-9939(03)07092-8
Keywords: Strictly hyperbolic operators, energy estimates, Log-Lipschitz continuity
Received by editor(s): September 30, 2002
Received by editor(s) in revised form: November 5, 2002
Published electronically: August 19, 2003
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2003 American Mathematical Society