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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

Author

Listed:
  • Abdelbaki Choucha

    (Department of Material Sciences, Faculty of Sciences, Amar Teleji Laghouat University, Laghouat 03000, Algeria
    Laboratory of Mathematics and Applied Sciences, Ghardaia University, Ghardaia 47000, 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 Research Center, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey)

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.

Suggested Citation

  • Abdelbaki Choucha & Salah Boulaaras & Ali Allahem & Asma Alharbi & Rashid Jan, 2024. "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," Mathematics, MDPI, vol. 12(17), pages 1-15, August.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2616-:d:1462915
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