Nonstandard Quasi-monotonicity: An Application to the Wave Existence in a Neutral KPP–Fisher Equation
- 48 Downloads
We revisit Wu and Zou non-standard quasi-monotonicity approach for proving existence of monotone wavefronts in monostable reaction–diffusion equations with delays. This allows to solve the problem of existence of monotone wavefronts in a neutral KPP–Fisher equation. In addition, using some new ideas proposed recently by Solar et al., we establish the uniqueness (up to a translation) of these monotone wavefronts.
KeywordsMonostable equation Quasi-monotonicity Non-standard order Uniqueness KPP–Fisher delayed equation Neutral differential equation
Mathematics Subject Classification34K12 35K57 92D25
This work was initiated during a research stay of S.T. at the São Paulo University at Ribeirão Preto, Brasil. It was supported by FAPESP (Brasil) Project 18/06658-1 and partially by FONDECYT (Chile) Project 1190712. The first author was supported by Fapesp (Brasil) Project 2017/13145-8. S.T. acknowledges the very kind hospitality of the DCM-USP and expresses his sincere gratitude to the Professors M. Pierri and E. Hernández for their support and hospitality.
- 8.Hernández, E., Trofimchuk, S.: Traveling wave solutions for partial neutral differential equations (2019) (submitted) Google Scholar
- 23.Volpert, V., Trofimchuk, S.: Global continuation of monotone waves for bistable delayed equations with unimodal nonlinearities. to appear (2019)Google Scholar
- 28.Wu, J., Zou, X.: Erratum to “Traveling wave fronts of reaction–diffusion systems with delays” [J . Dyn. Differ. Equ. 13, 651, 687 (2001)]. J. Dyn. Differ. Equ. 20, 531–533 (2008)Google Scholar