Well-posedness and exponential stability of a thermoelastic system with internal delay

ABSTRACT

The presence of a delay in a thermoelastic system destroys the well-posedness and the stabilizing effect of the heat conduction [1]. To avoid this problem, we add to the system, at the delayed equation, a Kelvin–Voigt damping. At first, we prove the well-posedness of the system by the semigroup theory. Next, under appropriate assumptions, we prove the exponential stability of the system by introducing a suitable Lyapunov functional.

Keywords:

• Thermoelastic system
• delay
• Kelvin–Voigt damping
• well-posedness
• exponential stability

2010 Mathematics Subject Classifications:

• 35B35
• 35B40
• 93D05 93D20

Disclosure statement

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