1509.01603v2.pdf (161.84 kB)
On hyperbolic systems with time dependent Holder characteristics
preprint
posted on 2016-01-14, 15:23 authored by Claudia Garetto, Michael RuzhanskyIn 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].
History
School
- Science
Department
- Mathematical Sciences
Citation
GARETTO, C. and RUZHANSKY, M., 2015. On hyperbolic systems with time dependent Holder characteristics. arXiv:1509.01603v2 [math.AP].Publisher
arXiv.orgVersion
- SMUR (Submitted Manuscript Under Review)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2015Notes
This pre-print was submitted to arXiv on 18 September 2015.Publisher version
Language
- en