Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T19:26:26.652Z Has data issue: false hasContentIssue false
  • English
  • Français

Analyticity of solutions for quasilinear wave equations and other quasilinear systems

Published online by Cambridge University Press:  01 December 2014

Sergei Kuksin  and
Nikolai Nadirashvili
Sergei Kuksin
Affiliation:
Université Paris 7, L'Unité de Formation et de Recherche de Mathématiques, 75205 Paris Cedex 13, France, ([email protected])
Nikolai Nadirashvili
Affiliation:
Centre National de la Recherche Scientifique et Université d'Aix-Marseille 1 – Laboratoire d'Analyse Topologie et Probabilités, 39 rue Frédéric Joliot-Curie, 13453 Marseille, France, ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove the persistence of analyticity for classical solutions of the Cauchy problem for quasilinear wave equations with analytic data. Our results show that the analyticity of solutions, stated by the Cauchy–Kowalewski and Ovsiannikov–Nirenberg theorems, lasts until a classical solution exists. Moreover, they show that if the equation and the Cauchy data are analytic only in a part of the space variables, then a classical solution is also analytic in these variables. The approach applies to other quasilinear equations and implies the persistence of the space analyticity (and the partial space analyticity) of their classical solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 6 , December 2014 , pp. 1155 - 1169
Copyright
Copyright © Royal Society of Edinburgh 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)