Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/18533

Title: On hyperbolic equations and systems with non-regular time dependent coefficients
Authors: Garetto, Claudia
Keywords: Hyperbolic equations
Hyperbolic systems
Gevrey spaces
Weak solutions
Issue Date: 2015
Publisher: © The Author. Published by Elsevier Inc.
Citation: GARETTO, C., 2015. On hyperbolic equations and systems with non-regular time dependent coefficients. Journal of Differential Equations, 259(11), pp.5846-5874.
Abstract: In this paper we study higher order weakly hyperbolic equations with time dependent non-regular coefficients. The non-regularity here means less than Hölder, namely bounded coefficients. As for second order equations in [14] we prove that such equations admit a ‘very weak solution’ adapted to the type of solutions that exist for regular coefficients. The main idea in the construction of a very weak solution is the regularisation of the coefficients via convolution with a mollifier and a qualitative analysis of the corresponding family of classical solutions depending on the regularising parameter. Classical solutions are recovered as limit of very weak solutions. Finally, by using a reduction to block Sylvester form we conclude that any first order hyperbolic system with non-regular coefficients is solvable in the very weak sense.
Description: This is an open access article published by Elsevier under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Sponsor: EPSRC First grant EP/L026422/1
Version: Published
DOI: 10.1016/j.jde.2015.07.011
URI: https://dspace.lboro.ac.uk/2134/18533
Publisher Link: http://dx.doi.org/doi:10.1016/j.jde.2015.07.011
ISSN: 1090-2732
Appears in Collections:Published Articles (Maths)

Files associated with this item:

File Description SizeFormat
garretto.pdfPublished version343.19 kBAdobe PDFView/Open


SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.