On boundary exact controllability of one‐dimensional wave equations with weak and strong interior degeneration

Language
en
Document Type
Article
Issue Date
2022-03-22
First published
2021-12-16
Issue Year
2021
Authors
Kogut, Peter I.
Kupenko, Olga P.
Leugering, Günter
Editor
Publisher
John Wiley & Sons Ltd
Abstract

In this paper, we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficient in the principle part of the elliptic operator. The objective is to provide a well‐posedness analysis of the corresponding system and derive conditions for its controllability through boundary actions. Passing to a relaxed version of the original problem, we discuss existence and uniqueness of solutions, and using the HUM method we derive conditions on the rate of degeneracy for both exact boundary controllability and the lack thereof.

Journal Title
Mathematical Methods in the Applied Sciences
Volume
45
Issue
2
Citation
Mathematical Methods in the Applied Sciences 45.2 (2022): S. 770-792. <https://onlinelibrary.wiley.com/doi/10.1002/mma.7811>
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