Well-posedness and exponential stability of coupled non-degenerate Kirchhoff and heat equations

ABSTRACT

This paper is consecrated to the asymptotic behavior of a coupled system consisting of the Kirchhoff and heat equations in a bounded domain. We establish that the problem is well-posed by using a Faedo–Galerkin scheme. Furthermore, the energy method combined with the multiplier techniques is used to show the exponential stability of the solutions to the system.

KEYWORDS:

• Coupled systems
• well-posedness
• Faedo–Galerkin
• decay estimates
• multiplier method
• integral inequalities

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35Q74
• 93D15
• 93D15
• 74J30

Disclosure statement

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