On hyperbolic systems with time dependent Hölder characteristics

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Title: On hyperbolic systems with time dependent Hölder characteristics
Author(s): Garetto, C
Ruzhansky, M
Item Type: Journal Article
Abstract: In this paper we study the well-posedness of weakly hyperbolic systems with time dependent coefficients. We assume that the eigenvalues are low regular, in the sense that they are H¨older with respect to t. In the past these kind of systems have been investigated by Yuzawa [15] and Kajitani [14] by employing semigroup techniques (Tanabe-Sobolevski method). Here, under a certain uniform property of the eigenvalues, we improve the Gevrey well-posedness result of [15] and we obtain well-posedness in spaces of ultradistributions as well. Our main idea is a reduction of the system to block Sylvester form and then the formulation of suitable energy estimates inspired by the treatment of scalar equations in.
Publication Date: 12-Apr-2016
Date of Acceptance: 11-Mar-2016
URI: http://hdl.handle.net/10044/1/30410
DOI: https://dx.doi.org/10.1007/s10231-016-0567-6
ISSN: 1618-1891
Publisher: Springer Verlag (Germany)
Start Page: 155
End Page: 164
Journal / Book Title: Annali di Matematica Pura ed Applicata
Volume: 196
Issue: 1
Copyright Statement: © The Author(s) 2016. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
RPG-2014-002
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Hyperbolic equations
Gevrey spaces
Ultradistributions
CAUCHY-PROBLEM
CONTINUOUS COEFFICIENTS
EQUATIONS
RESPECT
math.AP
math.AP
35L25, 35L40, 46F05
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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