A1 Journal article (refereed)
Well‐posedness and exponential stability for a nonlinear wave equation with acoustic boundary conditions (2024)

Bautista, G. J., Límaco, J., & Potenciano‐Machado, L. (2024). Well‐posedness and exponential stability for a nonlinear wave equation with acoustic boundary conditions. Mathematical Methods in the Applied Sciences, 47(2), 1132-1152. https://doi.org/10.1002/mma.9703

JYU authors or editors

Publication details

All authors or editors: Bautista, George J.; Límaco, Juan; Potenciano‐Machado, Leyter

Journal or series: Mathematical Methods in the Applied Sciences

ISSN: 0170-4214

eISSN: 1099-1476

Publication year: 2024

Publication date: 05/10/2023

Volume: 47

Issue number: 2

Pages range: 1132-1152

Publisher: John Wiley & Sons

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1002/mma.9703

Publication open access: Not open

Publication channel open access: 

Abstract

In this paper, we prove the well-posedness of a nonlinear wave equation coupled with boundary conditions of Dirichlet and acoustic type imposed on disjoints open boundary subsets. The proposed nonlinear equation models small vertical vibrations of an elastic medium with weak internal damping and a general nonlinear term. We also prove the exponential decay of the energy associated with the problem. Our results extend the ones obtained in previous results to allow weak internal dampings and removing the dimensional restriction 1≤n≤4. The method we use is based on a finite-dimensional approach by combining the Faedo-Galerkin method with suitable energy estimates and multiplier techniques.

Keywords: partial differential equations; wave motion

Free keywords: acoustic boundary conditions; energy estimates; Faedo-Galerkin method; multiplier method; non-linear evolution equation; stability

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2023

Preliminary JUFO rating: 1