Strong Stability for a Viscoelastic Transmission Problem Under a Nonlocal Boundary Control
Noureddine Touati Brahim,
Abderrahmane Beniani,
Abderrazak Chaoui,
Zayd Hajjej,
Perikles Papadopoulos,
Khaled Zennir
Affiliations
Noureddine Touati Brahim
Laboratoire de Mathématiques Appliquées et de Modélisation, Faculté de Mathématiques et de l’Informatique et des Sciences de la Matiére, Université 8 Mai 1945 Guelma, B.P. 401, Guelma 24000, Algeria
Abderrahmane Beniani
Engineering and Sustainable Development Laboratory, Faculty of Science and Technology, University of Ain Temouchent, Ain Temouchent 46000, Algeria
Abderrazak Chaoui
Laboratoire de Mathématiques Appliquées et de Modélisation, Faculté de Mathématiques et de l’Informatique et des Sciences de la Matiére, Université 8 Mai 1945 Guelma, B.P. 401, Guelma 24000, Algeria
Zayd Hajjej
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Perikles Papadopoulos
Department of Electrical and Electronics Engineering, University of West Attica, 11521 Athens, Greece
Khaled Zennir
Department of Mathematics, Faculty of Sciences, University 20 Août 1955, Skikda 21000, Algeria
The purpose of this paper is to consider a transmission problem of a viscoelastic wave with nonlocal boundary control. It should be noted that the present paper is based on the previous C. G. Gal and M. Warma works, together with H. Atoui and A. Benaissa. Namely, they focused on a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with an emphasis on rough interfaces and nonlinear dynamic (possibly, nonlocal) boundary conditions along the interface, where a transmission problem in the presence of a boundary control condition of a nonlocal type was investigated in these papers. Owing to the semigroup theory, we prove the question of well-posedness. For the very rare cases, we combined between the frequency domain approach and the Borichev–Tomilov theorem to establish strong stability results.
