Madani Douib, Mohamed Aidi

Well-Posedness and Exponential Stability of the Wave Equation with Delay and Thermodiffusion Effects

abstract:
In this paper, we consider a wave equation with delay term and thermodiffusion effects. At first, we prove the existence and uniqueness of the system by the semigroup theory. Next, under appropriate assumptions, we prove the exponential stability of the solution by introducing a suitable Lyapunov functional.

Mathematics Subject Classification: 35B35, 35B40, 93D05, 93D20

Key words and phrases: A wave equation, thermodiffusion effects, delay, well-posedness, exponential stability