Well-Posedness and Asymptotic Analysis of Wave Equation with Nonlocal Boundary Damping

Marcelo M. Cavalcanti; Adel M. Al-Mahdi; Mohammad M. Al-Gharabli; Cintya A. Okawa

doi:10.1007/s00245-025-10327-6

Well-Posedness and Asymptotic Analysis of Wave Equation with Nonlocal Boundary Damping

Marcelo M. Cavalcanti, Adel M. Al-Mahdi^*, Mohammad M. Al-Gharabli, Cintya A. Okawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this work, we study a wave equation with nonlocal boundary damping of energy type. We begin by establishing the well-posedness of the problem using the Galerkin method. Next, we investigate the asymptotic behavior of the solution by applying the multiplier method, and we enhance the decay rate through the use of Nakao’s Lemma. Finally, we employ the radial multiplier technique to obtain an optimal polynomial decay rate under this type of damping.

Original language	English
Article number	43
Journal	Applied Mathematics and Optimization
Volume	92
Issue number	2
DOIs	https://doi.org/10.1007/s00245-025-10327-6
State	Published - Oct 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

Keywords

Boundary damping
Energy damping
Galerkin method
Nakao’s lemma
Radial multiplier
Stability

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1007/s00245-025-10327-6

Cite this

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title = "Well-Posedness and Asymptotic Analysis of Wave Equation with Nonlocal Boundary Damping",

abstract = "In this work, we study a wave equation with nonlocal boundary damping of energy type. We begin by establishing the well-posedness of the problem using the Galerkin method. Next, we investigate the asymptotic behavior of the solution by applying the multiplier method, and we enhance the decay rate through the use of Nakao{\textquoteright}s Lemma. Finally, we employ the radial multiplier technique to obtain an optimal polynomial decay rate under this type of damping.",

keywords = "Boundary damping, Energy damping, Galerkin method, Nakao{\textquoteright}s lemma, Radial multiplier, Stability",

author = "Cavalcanti, \{Marcelo M.\} and Al-Mahdi, \{Adel M.\} and Al-Gharabli, \{Mohammad M.\} and Okawa, \{Cintya A.\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.",

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AU - Al-Mahdi, Adel M.

AU - Al-Gharabli, Mohammad M.

AU - Okawa, Cintya A.

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/10

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N2 - In this work, we study a wave equation with nonlocal boundary damping of energy type. We begin by establishing the well-posedness of the problem using the Galerkin method. Next, we investigate the asymptotic behavior of the solution by applying the multiplier method, and we enhance the decay rate through the use of Nakao’s Lemma. Finally, we employ the radial multiplier technique to obtain an optimal polynomial decay rate under this type of damping.

AB - In this work, we study a wave equation with nonlocal boundary damping of energy type. We begin by establishing the well-posedness of the problem using the Galerkin method. Next, we investigate the asymptotic behavior of the solution by applying the multiplier method, and we enhance the decay rate through the use of Nakao’s Lemma. Finally, we employ the radial multiplier technique to obtain an optimal polynomial decay rate under this type of damping.

KW - Boundary damping

KW - Energy damping

KW - Galerkin method

KW - Nakao’s lemma

KW - Radial multiplier

KW - Stability

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JO - Applied Mathematics and Optimization

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IS - 2

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ER -

Well-Posedness and Asymptotic Analysis of Wave Equation with Nonlocal Boundary Damping

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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