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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Parabolic evolution equations with asymptotically autonomous delay
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by Roland Schnaubelt PDF
Trans. Amer. Math. Soc. 356 (2004), 3517-3543 Request permission

Abstract:

We study retarded parabolic non-autonomous evolution equations whose coefficients converge as $t\to \infty$, such that the autonomous problem in the limit has an exponential dichotomy. Then the non-autonomous problem inherits the exponential dichotomy, and the solution of the inhomogeneous equation tends to the stationary solution at infinity. We use a generalized characteristic equation to deduce the exponential dichotomy and new representation formulas for the solution of the inhomogeneous equation.
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Additional Information
  • Roland Schnaubelt
  • Affiliation: FB Mathematik und Informatik, Martin-Luther-Universität, 06099 Halle, Germany
  • MR Author ID: 603222
  • Email: schnaubelt@mathematik.uni-halle.de
  • Received by editor(s): January 18, 2002
  • Received by editor(s) in revised form: March 27, 2003
  • Published electronically: November 25, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 3517-3543
  • MSC (2000): Primary 35R10; Secondary 34K30, 47D06
  • DOI: https://doi.org/10.1090/S0002-9947-03-03512-8
  • MathSciNet review: 2055745