This paper is concerned with transition fronts for reaction-diffusion equations of the Fisher-KPP type. Basic examples of transition fronts connecting the unstable steady state to the stable one are the standard traveling fronts, but the class of transition fronts is much larger and the dynamics of the solutions of such equations is very rich. In the paper, we describe the class of transition fronts and we study their qualitative dynamical properties. In particular, we characterize the set of their admissible asymptotic past and future speeds and their asymptotic profiles and we show that the transition fronts can only accelerate. We also classify the transition fronts in the class of measurable superpositions of standard traveling fronts.

Transition fronts for the fisher-KPP equation / Hamel, F.; Rossi, L.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 368:12(2016), pp. 8675-8713. [10.1090/tran/6609]

Transition fronts for the fisher-KPP equation

Rossi L.
2016

Abstract

This paper is concerned with transition fronts for reaction-diffusion equations of the Fisher-KPP type. Basic examples of transition fronts connecting the unstable steady state to the stable one are the standard traveling fronts, but the class of transition fronts is much larger and the dynamics of the solutions of such equations is very rich. In the paper, we describe the class of transition fronts and we study their qualitative dynamical properties. In particular, we characterize the set of their admissible asymptotic past and future speeds and their asymptotic profiles and we show that the transition fronts can only accelerate. We also classify the transition fronts in the class of measurable superpositions of standard traveling fronts.
2016
Generalized traveling-waves; spreading speeds; variational principle; diffusion; propagation; convergence; existence
01 Pubblicazione su rivista::01a Articolo in rivista
Transition fronts for the fisher-KPP equation / Hamel, F.; Rossi, L.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 368:12(2016), pp. 8675-8713. [10.1090/tran/6609]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1464667
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