Global stability of noncritical traveling front solutions of Fisher-type equations with degenerate nonlinearity

2021 ◽  
Vol 62 (5) ◽  
pp. 051506
Author(s):  
Yang Wang ◽  
Xinyue Cao ◽  
Zhaohai Ma ◽  
Xiong Li
Keyword(s):  
Global Stability ◽  
Front Solutions ◽  
Traveling Front

scholarly journals Global Stability of Traveling Waves for a More General Nonlocal Reaction-Diffusion Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Rui Yan ◽  
Guirong Liu
Keyword(s):  
Diffusion Equation ◽  
Global Stability ◽  
Reaction Diffusion ◽  
Rates Of Convergence ◽  
Decay Rates ◽  
Reaction Diffusion Equation ◽  
Weighted Energy Method ◽  
Front Solutions ◽  
Traveling Front ◽  
Nonlocal Reaction

The purpose of this paper is to investigate the global stability of traveling front solutions with noncritical and critical speeds for a more general nonlocal reaction-diffusion equation with or without delay. Our analysis relies on the technical weighted energy method and Fourier transform. Moreover, we can get the rates of convergence and the effect of time-delay on the decay rates of the solutions. Furthermore, according to the stability results, the uniqueness of the traveling front solutions can be proved. Our results generalize and improve the existing results.

A SIMPLIFIED MODEL OF PROPAGATION AND DISSIPATION OF EXCITATION FRONTS

2003 ◽  
Vol 13 (12) ◽  
pp. 3605-3619 ◽  
Author(s):  
V. N. BIKTASHEV
Keyword(s):  
Cardiac Tissue ◽  
Simplified Model ◽  
Excitation Wave ◽  
Temporal Gradient ◽  
Transmembrane Voltage ◽  
Front Solutions ◽  
Traveling Front ◽  
Order Of Magnitude ◽  
Na Inactivation ◽  
Simplified Mathematical Model

An excitation wave in nerve or cardiac tissue may fail to propagate if the temporal gradient of the transmembrane voltage at the front becomes too small to excite the tissue ahead of it. A simplified mathematical model is suggested, that reproduces this phenomenon and has exact traveling front solutions. The spectrum of possible propagation speeds is bounded from below. This causes a front to dissipate if it is not allowed to propagate quickly enough. A crucial role is played by the Na inactivation gates, even if their dynamics are by an order of magnitude slower than the dynamics of the voltage.

Sign in / Sign up

Export Citation Format

Share Document