Global attractor for a degenerate Klein–Gordon–Schrödinger-type system

Abstract

In this paper, we study the long-time behaviour of solutions of a degenerate Klein–Gordon–Schrödinger-type system which is defined in a bounded domain. First, we proved the existence, uniqueness and continuity of the solutions on the initial data, then the asymptotic compactness of the solutions and finally the existence of a global compact attractor.

Keywords:

• Klein–Gordon–Schrödinger system
• global attractor
• absorbing set
• continuity
• asymptotic compactness

AMS Subject Classifications:

• 35B40
• 35B45

Acknowledgments

The authors would like to thank the referee for the fruitful suggestions which improved the original result and presentation of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).