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Transactions of the American Mathematical Society

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

 

 

Global boundedness for a delay-differential equation


Author: Stephan Luckhaus
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0825736-7
Article copyright: © Copyright 1986 American Mathematical Society