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Entire solutions of the KPP equation

โœ Scribed by F. Hamel; N. Nadirashvili

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
200 KB
Volume
52
Category
Article
ISSN
0010-3640

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โœฆ Synopsis

This paper deals with the solutions defined for all time of the KPP equation

where f is a KPP-type nonlinearity defined in [0, 1]:

. This equation admits infinitely many traveling-wave-type solutions, increasing or decreasing in x. It also admits solutions that depend only on t. In this paper, we build four other manifolds of solutions: One is 5-dimensional, one is 4-dimensional, and two are 3-dimensional. Some of these new solutions are obtained by considering two traveling waves that come from both sides of the real axis and mix. Furthermore, the traveling-wave solutions are on the boundary of these four manifolds.

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