Well-posedness and decay of solution for a transmission problem in the presence of infinite history and varying delay

  • Abdelouaheb Ardjouni University of Annaba, Department of Mathematics
  • Salah Zitouni
  • Khaled Zennir
  • Rachida Amiar

Abstract

In this article we consider a transmission problem in a bounded domain with a varying delay term and the presence of infinite history in the first equation. Under suitable assumptions on the weight of the damping and the weight of the delay, we prove the existence and the uniqueness of the solution using the semigroup theory. Also we show the exponential stability of the solution by introducing a suitable Lyaponov functional.

Published
May 28, 2018
How to Cite
ARDJOUNI, Abdelouaheb et al. Well-posedness and decay of solution for a transmission problem in the presence of infinite history and varying delay. Nonlinear Studies, [S.l.], v. 25, n. 2, p. 445-465, may 2018. ISSN 2153-4373. Available at: <http://nonlinearstudies.com/index.php/nonlinear/article/view/1585>. Date accessed: 25 june 2018.