Traveling Waves Impulses of FitzHugh Model with Diffusion and Cross-Diffusion

2016 ◽  
pp. 1-20
Author(s):  
Faina Berezovskaya
Keyword(s):  
Traveling Waves ◽  
Cross Diffusion

scholarly journals Cross-diffusion and traveling waves in porous-media flux-saturated Keller–Segel models

2018 ◽  
Vol 28 (11) ◽  
pp. 2103-2129 ◽  
Author(s):  
Margarita Arias ◽  
Juan Campos ◽  
Juan Soler
Keyword(s):  
Porous Media ◽  
Traveling Waves ◽  
Finite Time ◽  
Blow Up ◽  
Type Systems ◽  
Jump Discontinuity ◽  
Qualitative Properties ◽  
Cross Diffusion ◽  
Constants Of Motion ◽  
Diffusion Mechanisms

This paper deals with the analysis of qualitative properties involved in the dynamics of Keller–Segel type systems in which the diffusion mechanisms of the cells are driven by porous-media flux-saturated phenomena. We study the regularization inside the support of a solution with jump discontinuity at the boundary of the support. We analyze the behavior of the size of the support and blow-up of the solution, and the possible convergence in finite time toward a Dirac mass in terms of the three constants of the system: the mass, the flux-saturated characteristic speed, and the chemoattractant sensitivity constant. These constants of motion also characterize the dynamics of regular and singular traveling waves.

Sign in / Sign up

Export Citation Format

Share Document