Note on exponential and polynomial convergence for a delayed wave equation without displacement
Year: 2018
Type: preprint
Abstract: This note places primary emphasis on improving the asymptotic behavior of a multi-dimensional delayed wave equation in the absence of any displacement term. In the first instance, the delay is assumed to occur in the boundary. Then, invoking a geometric condition BLR on the domain, the exponential convergence of solutions to their equilibrium state is proved. The strategy adopted of the proof is based on an interpolation inequality combined with a resolvent method. In turn, an internal delayed wave equation is considered in the second case, where the domain possesses trapped ray and hence (BLR) geometric condition does not hold. In such a situation polynomial convergence results are established. These finding improve earlier results of Ammari-Chentouf and Phung.
Source: arXiv (Cornell University)
Authors: Ammari, Kaïs, Chentouf, Boumediène
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Kuwait University
Award: G7716909232
OpenAlex ID: W2798148089