TY - JOUR
A2 - Li, Tongxing
AU - Sánchez-Garduño, Faustino
AU - Pérez-Velázquez, Judith
PY - 2016
DA - 2016/09/01
TI - Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations
SP - 5620839
VL - 2016
AB - This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0)=0) and advection-degenerate (at h′(0)=0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1) h′(u) is constant k, (2) h′(u)=ku with k>0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k=0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE.
SN - 2356-6140
UR - https://doi.org/10.1155/2016/5620839
DO - 10.1155/2016/5620839
JF - The Scientific World Journal
PB - Hindawi Publishing Corporation
KW -
ER -