On hyperbolic systems with time dependent Hölder characteristics

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Title: On hyperbolic systems with time dependent Hölder characteristics
Author(s): Ruzhansky, M
Garetto, C
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: 1-Feb-2017
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)
Journal / Book Title: Annali di Matematica Pura ed Applicata
Copyright Statement: © The Author(s) 2016. This article is published with open access at Springerlink.com
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
Keywords: General Mathematics
0101 Pure Mathematics
Publication Status: Accepted
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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