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An extension of Wright's 3/2-theorem for the KPP-Fisher delayed equation


Authors: Karel Hasik and Sergei Trofimchuk
Journal: Proc. Amer. Math. Soc. 143 (2015), 3019-3027
MSC (2010): Primary 34K10, 35K57; Secondary 92D25
DOI: https://doi.org/10.1090/S0002-9939-2015-12496-3
Published electronically: February 13, 2015
MathSciNet review: 3336626
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Abstract: We present a short proof of the following natural extension of Wright's famous $ 3/2$-stability theorem: the conditions $ \tau \leq 3/2, \ c \geq 2$ imply the presence of the positive traveling fronts (not necessarily monotone) $ u = \phi (x\cdot \nu +ct), \ \vert\nu \vert =1,$ in the delayed KPP-Fisher equation $ u_t(t,x) = \Delta u(t,x) + u(t,x)(1-u(t-\tau ,x)), $ $ u \geq 0,$ $ x \in \mathbb{R}^m.$


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Additional Information

Karel Hasik
Affiliation: Mathematical Institute, Silesian University, 746 01 Opava, Czech Republic
Email: Karel.Hasik@math.slu.cz

Sergei Trofimchuk
Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
Email: trofimch@inst-mat.utalca.cl

DOI: https://doi.org/10.1090/S0002-9939-2015-12496-3
Keywords: KPP-Fisher equation, Wright's 3/2-theorem, delay
Received by editor(s): February 5, 2013
Received by editor(s) in revised form: March 7, 2014
Published electronically: February 13, 2015
Additional Notes: This research was realized within the framework of the OPVK program, project CZ.1.07/2.300/20.0002
The second author was also partially supported by FONDECYT (Chile), project 1110309, and by CONICYT (Chile) through PBCT program ACT-56.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society

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