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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Global boundedness for a delay-differential equation
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by Stephan Luckhaus PDF
Trans. Amer. Math. Soc. 294 (1986), 767-774 Request permission

Abstract:

The inequality $({\partial _t}u - \Delta u)(t, x)\qquad \leq \qquad u(t, x)(1 - u(t - \tau , x))$ is investigated. It is shown that nonnegative solutions of the Dirichlet problem in a bounded interval remain bounded as time goes to infinity, whereas in a more dimensional domain, in general, this holds only if the delay is not too large.
References
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 767-774
  • MSC: Primary 35B40; Secondary 35R10
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825736-7
  • MathSciNet review: 825736