TY - JOUR
T1 - On the existence of non-monotone non-oscillating wavefronts
AU - Ivanov, Anatoli
AU - Gomez, Carlos
AU - Trofimchuk, Sergei
N1 - Funding Information:
The authors express their gratitude to the handling editor and to the two anonymous referees for their valuable comments and suggestions which helped to improve the final version of this paper. This research was supported in part by the CONICYT grant 80110006 (A. Ivanov) and the FONDECYT grant 1110309 (S. Trofimchuk and C. Gomez). S. Trofimchuk also acknowledges support from CONICYT PBCT program ACT-56 . C. Gomez was supported by the CONICYT grant 21110243 , program “Becas para Estudios de Doctorado en Chile”. We would like to thank Penn State student Valerie Lindner for her computational and graphical work, some of which is used in this paper. She has done this work within a PSU W-B undergraduate student research project.
PY - 2014/11/1
Y1 - 2014/11/1
N2 - We present a monostable delayed reaction-diffusion equation with the unimodal birth function which admits only non-monotone wavefronts. Moreover, these fronts are either eventually monotone (in particular, such is the minimal wave) or slowly oscillating. Hence, for the Mackey-Glass type diffusive equations, we answer affirmatively the question about the existence of non-monotone non-oscillating wavefronts. As it was recently established by Hasik et al. and Ducrot et al., the same question has a negative answer for the KPP-Fisher equation with a single delay.
AB - We present a monostable delayed reaction-diffusion equation with the unimodal birth function which admits only non-monotone wavefronts. Moreover, these fronts are either eventually monotone (in particular, such is the minimal wave) or slowly oscillating. Hence, for the Mackey-Glass type diffusive equations, we answer affirmatively the question about the existence of non-monotone non-oscillating wavefronts. As it was recently established by Hasik et al. and Ducrot et al., the same question has a negative answer for the KPP-Fisher equation with a single delay.
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U2 - 10.1016/j.jmaa.2014.04.075
DO - 10.1016/j.jmaa.2014.04.075
M3 - Article
AN - SCOPUS:84902363132
SN - 0022-247X
VL - 419
SP - 606
EP - 616
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -