Asymptotic behavior and traveling wave solutions for parabolic functional-differential equations

Schaaf, Klaus W.

doi:10.1090/S0002-9947-1987-0891637-2

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

Asymptotic behavior and traveling wave solutions for parabolic functional-differential equations

Author: Klaus W. Schaaf
Journal: Trans. Amer. Math. Soc. 302 (1987), 587-615
MSC: Primary 35R10; Secondary 35B40, 35K55
MathSciNet review: 891637
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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.

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