TY - JOUR
T1 - Internal feedback stabilization of multi-dimensional wave equations with a boundary delay
T2 - a numerical study
AU - Ammari, Kaïs
AU - Chentouf, Boumediène
AU - Smaoui, Nejib
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/2/14
Y1 - 2022/2/14
N2 - In this paper, we consider two internal stabilization problems for the multi-dimensional wave equation with a boundary time-delay. We prove that the first problem is well-posed in an appropriate functional space. Subsequently, we numerically study the exponential stability in a two-dimensional case under Geometric Control Condition (GCC) derived by Lebeau. In addition, we provide a numerical investigation of the second wave system, which corresponds to the two-dimensional variant of the system studied by Datko et al.
AB - In this paper, we consider two internal stabilization problems for the multi-dimensional wave equation with a boundary time-delay. We prove that the first problem is well-posed in an appropriate functional space. Subsequently, we numerically study the exponential stability in a two-dimensional case under Geometric Control Condition (GCC) derived by Lebeau. In addition, we provide a numerical investigation of the second wave system, which corresponds to the two-dimensional variant of the system studied by Datko et al.
KW - Boundary delay
KW - Internal stabilization
KW - Wave equations
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U2 - 10.1186/s13661-022-01589-y
DO - 10.1186/s13661-022-01589-y
M3 - Article
AN - SCOPUS:85124951558
SN - 1687-2762
VL - 2022
JO - Boundary Value Problems
JF - Boundary Value Problems
IS - 1
M1 - 8
ER -