Stability of traveling wave fronts for delayed Belousov–Zhabotinskii models with spatial diffusion

ABSTRACT

This paper is concerned with the stability of traveling wave fronts of a delayed Belousov–Zhabotinskii model with spatial diffusion. The existence and comparison theorem of solutions of the corresponding Cauchy problem in a weight space are established for the system on $\mathbb{R}$ by appealing to the theories of semigroup and abstract functional differential equations. By means of comparison principle and the weighted energy method, we prove that the traveling wave solutions are exponentially stable, when the initial perturbation around the traveling waves decays exponentially as $x\to -\mathrm{\infty }$, but in other locations, the initial data can be arbitrarily large.

COMMUNICATED BY:

• Ming Mei

KEYWORDS:

• Stability
• Belousov–Zhabotinskii model
• comparison principle
• weighted energy method
• traveling wave fronts

AMS SUBJECT CLASSIFICATIONS:

• 35C07
• 92D25
• 35B35

Acknowledgements

We are grateful to two anonymous referees for their careful reading and helpful suggestions which led to an improvement of our original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of W. G. Zhang was partially supported by National Natural Science Foundation of China (No. 11471215), by Shanghai Leading Academic Discipline Project (No. XTKX2012) and by the Hujiang Foundation of China (B14005). The research of Z. X. Yu was partially supported by Natural Science Foundation of Shanghai (No. 18ZR1426500).