Results from a Nonlinear Wave Equation with Acoustic and Fractional Boundary Conditions Coupling by Logarithmic Source and Delay Terms: Global Existence and Asymptotic Behavior of Solutions

Abdelbaki Choucha, Salah Boulaaras (), Ali Allahem, Asma Alharbi and Rashid Jan
Additional contact information
Abdelbaki Choucha: Department of Material Sciences, Faculty of Sciences, Amar Teleji Laghouat University, Laghouat 03000, Algeria
Salah Boulaaras: Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
Ali Allahem: Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
Asma Alharbi: Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
Rashid Jan: Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, Kajang 43000, Selangor, Malaysia

Mathematics, 2024, vol. 12, issue 17, 1-15

Abstract: The nonlinear wave equation with acoustic and fractional boundary conditions, coupled with logarithmic source and delay terms, is significant for its ability to model complex systems, its contribution to the advancement of mathematical theory, and its wide-ranging applicability to real-world problems. This paper examines the global existence and general decay of solutions to a wave equation characterized by coupling with logarithmic source and delay terms, and governed by both fractional and acoustic boundary conditions. The global existence of solutions is analyzed under a range of hypotheses, and the general decay behavior is established through the construction and application of an appropriate Lyapunov function.

Keywords: wave equation; global existence; partial differential equations; Lyapunov function; general decay; fractional boundary dissipation; acoustic boundary conditions; logarithmic source (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/17/2616/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/17/2616/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:17:p:2616-:d:1462915

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().