EXISTENCE AND STABILITY OF A DAMPED WAVE EQUATION WITH TWO DELAYED TERMS IN BOUNDARY

SALAH  ZITOUNI; ABDELOUAHEB  ARDJOUNI; KHALED ZENNIR; RACHIDA AMIAR

EXISTENCE AND STABILITY OF A DAMPED WAVE EQUATION WITH TWO DELAYED TERMS IN BOUNDARY

Authors

SALAH ZITOUNI Department of Mathematics and Informatics, University of Souk-Ahras, Souk-Ahras
ABDELOUAHEB ARDJOUNI Department of Mathematics and Informatics, University of Souk-Ahras, Souk-Ahras
KHALED ZENNIR Department of Mathematics, University of Skikda
RACHIDA AMIAR Department of Mathematics, Faculty of Sciences, University of Annaba, Annaba

Keywords:

Damped wave equation, delay feedback, stabilization, semigroup formulation

Abstract

This paper considers a linear damped wave equation with dynamic boundary conditions where two feedback terms have a delay. In bounded domain, we first establish the question of well-posedness and uniqueness of the solution for the initial-boundary value problem, using semigroup arguments in <cite>kato:67,kato:76,pazy</cite>. Next, by introducing suitable Lyapunov functionals, exponential stability estimates are obtained under conditions on the delay terms.