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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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Asymptotic behavior and traveling wave solutions for parabolic functional-differential equations
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by Klaus W. Schaaf PDF
Trans. Amer. Math. Soc. 302 (1987), 587-615 Request permission

Abstract:

This paper is a generalization of the theory of the KPP and bistable nonlinear diffusion equations. It is shown that traveling wave solutions exist for nonlinear parabolic functional differential equations (FDEs) which behave very much like the well-known solutions of the classical KPP and bistable equations. Among the techniques used are maximum principles, sub- and supersolutions, phase plane techniques for FDEs and perturbation of linear operators.
References
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 302 (1987), 587-615
  • MSC: Primary 35R10; Secondary 35B40, 35K55
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0891637-2
  • MathSciNet review: 891637