Exponential decay and well-posedness for a one-dimensional porous-elastic system with distributed delay

Abstract

In this paper, we consider a one-dimensional porous-elastic system with distributed delay term acting on the porous equation. Under suitable assumptions on the weight of distributed delay, we establish the well-posedness of the system by using semigroup theory and we show that the dissipation given by this complementary control stabilizes exponentially the system for the case of equal speeds of wave propagation.

COMMUNICATED BY:

• M. Fang

Keywords:

• Porous-elastic system
• semigroup theory
• distributed delay
• exponential stability
• Lyapunov method

2010 Mathematics Subject Classifications:

• 35L70
• 35B40
• 93D20

Acknowledgements

The authors wish to thank deeply the anonymous referee for useful remarks and careful reading of the proofs presented in this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.