Global stability of traveling waves for non-monotone lattice differential equations with time-delay

ABSTRACT

This paper is concerned with the global stability of traveling waves for non-monotone infinite-dimensional lattice differential equations with time delay. By establishing the boundedness estimate of the solution of the perturbation equation, we obtain that, for any initial perturbations around the traveling wave, the noncritical traveling waves are globally stable with the exponential convergence rate $t^{-1/\alpha }{e}^{-\mu t}(\mu >0\mathrm{a}\mathrm{n}\mathrm{d}0<\alpha \le 2)$, and the critical traveling waves are globally stable with the algebraic convergence rate $t^{-1/\alpha }$ in a weighted Sobolev space.

Keywords:

• Lattice differential equations
• traveling wave solutions
• global stability
• weighted energy
• time delay

2010 Mathematics Subject Classifications:

• 34A33
• 35C07
• 39A11
• 35A25

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the NNSF of China [grant numbers 11371179, 11731005].