Traveling waves for a fisher-type reaction-diffusion equation with a flux in divergence form
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Show full item recordEditorial
World scientific publ co pte ltd
Date
2022-07-13Referencia bibliográfica
Published version: Arias, M., & Campos, J. (2022). Traveling waves for a Fisher-type reaction-diffusion equation with a flux in divergence form. Mathematical Models and Methods in Applied Sciences[https://doi.org/10.1142/S0218202523500318]
Sponsorship
Spanish Government RTI2018-098850-B-I00; Junta de Andalucia PY18-RT-2422 B-FQM-580-UGR20 A-FQM-311-UGR18Abstract
Abstract. Analysis of the speed of propagation in parabolic operators is frequently
carried out considering the minimal speed at which its traveling waves
move. This value depends on the solution concept being considered.
We analyze an extensive class of Fisher-type reaction-di usion equations
with
ows in divergence form. We work with regular
ows, which may not meet
the standard elliptical conditions, but without other types of singularities.
We show that the range of speeds at which classic traveling waves move is
an interval unbounded to the right. Contrary to classic examples, the in mum
may not be reached. When the
ow is elliptic or over-elliptic, the minimum
speed of propagation is achieved.
The classic traveling wave speed threshold is complemented by another
value by analyzing an extension of the rst order boundary value problem to
which the classic case is reduced. This singular minimum speed can be justi ed
as a viscous limit of classic minimal speeds in elliptic or over-elliptic
ows.
We construct a singular pro le for each speed between the minimum singular
speed and the speeds at which classic traveling waves move. Under
additional assumptions, the constructed pro le can be justi ed as that of a
traveling wave of the starting equation in the framework of bounded variation
functions.
We also show that saturated fronts verifying the Rankine-Hugoniot condition
can appear for strictly lower speeds even in the framework of bounded
variation functions.