Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems

28Citations
Citations of this article
4Readers
Mendeley users who have this article in their library.
Get full text

Abstract

We consider a spatially homogeneous system of reaction-diffusion equation defined on the interval (-∞, ∞) of the one-dimensional spatial variable x. It is known that this equation has a one-parameter family of periodic travelling wave solutions Ψ(x + ct; c) if this equation has a spatially homogeneous periodic solution φ(t). The spatial period L(c) of the travelling wave solution satisfies L(c) c → T if c → +∞, where c is the propagation speed and T is the period of φ(t). We prove that, in the case c > 0 is sufficiently large, Ψ(x + ct; c) is unstable if φ(t) is "strongly unstable" and Ψ(x + ct; c) is "marginally stable" if φ(t) is "strongly stable." If the equation is defined on a finite interval [0, l] of the variable x with the periodic boundary conditions, we can obtain a more precise result regarding the stability of Ψ(x + c ̂t; c ̂), where c ̂ > 0 is a speed which satisfies l = mL( c ̂) for some positive integer m. We prove that this solution is asymptotically stable in the sense of waveform stability if c ̂ > 0 is sufficiently large and if φ(t) is "strongly stable.". © 1981.

Cite

CITATION STYLE

APA

Maginu, K. (1981). Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems. Journal of Differential Equations, 39(1), 73–99. https://doi.org/10.1016/0022-0396(81)90084-X

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free