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

Loughborough University Institutional Repository

 Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/28240

 Title: Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I. Well-posedness Authors: Garetto, ClaudiaJah, ChristianRuzhansky, Michael Keywords: Hyperbolic systemsFourier integral operatorsSobolev spaces Issue Date: 2018 Publisher: arXiv.org Citation: GARETTO, C., JAH, C. and RUZHANSKY, M., 2018. Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I. Well-posedness. arXiv:1801.03573v1 [math.AP]. Abstract: In this paper we analyse the well-posedness of the Cauchy problem for a rather general class of hyperbolic systems with space-time dependent coefficients and with multiple characteristics of variable multiplicity. First, we establish a well-posedness result in anisotropic Sobolev spaces for systems with upper triangular principal part under interesting natural conditions on the orders of lower order terms below the diagonal. Namely, the terms below the diagonal at a distance $k$ to it must be of order $-k$. This setting also allows for the Jordan block structure in the system. Second, we give conditions for the Schur type triangularisation of general systems with variable coefficients for reducing them to the form with an upper triangular principal part for which the first result can be applied. We give explicit details for the appearing conditions and constructions for $2\times 2$ and $3\times 3$ systems, complemented by several examples. Description: This pre-print was submitted to arXiv on 10 January 2018. Sponsor: The third author was supported in parts by EPSRC grant EP/R003025/1 and by the Leverhulme Grant RPG-2017-151. Version: Submitted for publication URI: https://dspace.lboro.ac.uk/2134/28240 Publisher Link: https://arxiv.org/abs/1801.03573 Appears in Collections: Pre-prints (Maths)

Files associated with this item:

File Description SizeFormat