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