Ruikson S. O. Nunes, Miguel R. Nunez-Chavez
Abstract:
The purpose of this article is to study exact boundary problems for the
standard wave equation in domains that are the exterior of a convex
compact set of \(\mathbb{R}^2\), where both have a common boundary part.
We consider two cases: first where the boundary domain is fixed,
and where a part of the boundary is moving.
In both cases we consider control problems with controls acting only
one part of the boundary. For the fixed boundary case the control
is of Neumann type, and for the moving boundary case the control is
a conormal derivative type.
The controllability method used here was developed by Russell [17].
Submitted November 21, 2024. Published March 4, 2025.
Math Subject Classifications: 35L05, 35L20, 35L53, 35B40, 93B05, 49J20.
Key Words: Wave equation; energy decay; exact boundary controllability; non-cylindrical domains; moving boundary domains
DOI: 10.58997/ejde.2025.25
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Ruikson S. O. Nunes UFMT- Federal University of Mato Grosso, ICET Department of Mathematics, 78060-900 Cuiabá, MT, Brazil email: ruiksonsillas@hotmail.com |
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Miguel R. Nuñez-Chávez UFMT- Federal University of Mato Grosso, ICET Department of Mathematics, 78060-900 Cuiabá, MT, Brazil email: miguel.chavez@ufmt.br |
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