Hostname: page-component-cb9f654ff-kl2l2 Total loading time: 0 Render date: 2025-08-30T10:29:37.679Z Has data issue: false hasContentIssue false
  • English
  • Français

Abstract Cauchy problems for quasi-linear evolution equations in the sense of Hadamard

Published online by Cambridge University Press:  30 June 2004

Naoki Tanaka
Naoki Tanaka
Affiliation:
Department of Mathematics, Faculty of Science, Okayama University, Okayama 700-8530, Japan. E-mail: tanaka@math.okayama-u.ac.jp
Get access

Abstract

This paper is devoted to the well-posedness of abstract Cauchy problems for quasi-linear evolution equations. The notion of Hadamard well-posedness is considered, and a new type of stability condition is introduced from the viewpoint of the theory of finite difference approximations. The result obtained here generalizes not only some results on abstract Cauchy problems closely related with the theory of integrated semigroups or regularized semigroups but also the Kato theorem on quasi-linear evolution equations. An application to some quasi-linear partial differential equation of weakly hyperbolic type is also given.

Keywords

abstract Cauchy problem in the sense of Hadamardregularized semigroupabstract quasi-linear evolution equationstability conditionfinite difference approximation34G2047J25 (primary)47D6047D62 (secondary)

Information

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 89 , Issue 1 , July 2004 , pp. 123 - 160
Copyright
2004 London Mathematical Society

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.)

Article purchase

Temporarily unavailable