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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/20042

Title: On hyperbolic systems with time dependent Holder characteristics
Authors: Garetto, Claudia
Ruzhansky, Michael
Issue Date: 2015
Publisher: arXiv.org
Citation: GARETTO, C. and RUZHANSKY, M., 2015. On hyperbolic systems with time dependent Holder characteristics. arXiv:1509.01603v2 [math.AP].
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 Holder with respect to t. In the past these kind of systems have been investigated by Yuzawa [Yuz05] and Kajitani [KY06] by employing semigroup techniques (Tanabe-Sobolevski method). Here, under a certain uniform property of the eigenvalues, we improve the Gevrey well-posedness result of [Yuz05] 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 [GR12].
Description: This pre-print was submitted to arXiv on 18 September 2015.
Version: Submitted for publication
URI: https://dspace.lboro.ac.uk/2134/20042
Publisher Link: http://arxiv.org/abs/1509.01603
Appears in Collections:Pre-prints (Maths)

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