WELL-POSEDNESS AND ASYMPTOTIC STABILITY OF SOLUTIONS TO A BRESSE SYSTEM WITH TIME VARYING DELAY TERMS AND INFINITE MEMORIES

Abstract

We consider the Bresse system in bounded domain with timevarying delay terms in the internal feedbacks and innite memories acting in the three equations of the system. First, we prove the well-posedness of its solutions in Sobolev spaces by means of semigroup theory. Furthermore, the asymptotic stability is also discussed by using an appropriate Lyapunovfunctional.We consider the Bresse system in bounded domain with timevarying delay terms in the internal feedbacks and innite memories actingin the three equations of the system. First, we prove the well-posedness ofits solutions in Sobolev spaces by means of semigroup theory. Furthermore,the asymptotic stability is also discussed by using an appropriate Lyapunovfunctional.