Skip to Main Content

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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Global boundedness for a delay-differential equation
HTML articles powered by AMS MathViewer

by Stephan Luckhaus
Trans. Amer. Math. Soc. 294 (1986), 767-774
DOI: https://doi.org/10.1090/S0002-9947-1986-0825736-7

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
  • David Green Jr. and Harlan W. Stech, Diffusion and hereditary effects in a class of population models, Differential equations and applications in ecology, epidemics, and population problems (Claremont, Calif., 1981) Academic Press, New York-London, 1981, pp. 19–28. MR 645186
  • Juan Lin and Peter B. Kahn, Random effects in population models with hereditary effects, J. Math. Biol. 10 (1980), no. 2, 101–112. MR 596461, DOI 10.1007/BF00275836
  • A. Tesei, Stability properties for partial Volterra integro-differential equations, Ann. Mat. Pura Appl. (4) 126 (1980), 103–115 (1981). MR 612355, DOI 10.1007/BF01762503
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 35B40, 35R10
  • Retrieve articles in all journals with MSC: 35B40, 35R10
Bibliographic 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