Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Generation of linear evolution operators

Author: Naoki Tanaka
Journal: Proc. Amer. Math. Soc. 128 (2000), 2007-2015
MSC (1991): Primary 47D06; Secondary 34G10
Published electronically: November 24, 1999
MathSciNet review: 1654080
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is devoted to the problem of generation of evolution operators associated with linear evolution equations in a general Banach space. The stability condition is proposed from the viewpoint of finite difference approximations. It is shown that linear evolution operators can be generated even if the stability condition given here is assumed instead of Kato's stability condition.

References [Enhancements On Off] (What's this?)

  • 1. T. Kato, Linear evolution equations of ``hyperbolic" type, J. Fac. Sci. Univ. Tokyo 17 (1970), 241-258. MR 43:5347
  • 2. T. Kato, Abstract evolution equations, linear and quasilinear, revisited, Lecture Notes in Math. 1540 (1993), 103-125. MR 95m:34108
  • 3. K. Kobayasi, On a theorem for linear evolution equations of hyperbolic type, J. Math. Soc. Japan 31 (1979), 647-654. MR 81a:34051
  • 4. K. Kobayasi and N. Sanekata, A method of iterations for quasi-linear evolution equations in nonreflexive Banach spaces, Hiroshima Math J. 19 (1989), 521-540. MR 91a:34048

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47D06, 34G10

Retrieve articles in all journals with MSC (1991): 47D06, 34G10

Additional Information

Naoki Tanaka
Affiliation: Department of Mathematics, Faculty of Science, Okayama University, Okayama 700-8530, Japan

Keywords: Linear evolution operator, stability condition, intertwining condition
Received by editor(s): May 4, 1998
Received by editor(s) in revised form: August 24, 1998
Published electronically: November 24, 1999
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society