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Blow-Up of Solution of Lamé Wave Equation with Fractional Damping and Logarithmic Nonlinearity Source Terms

Author

Listed:
  • Amina Benramdane

    (Higher School of Management, Tlemcen 13000, Algeria
    Statistic and Random Modelization Laboratory, Tlemcen 13000, Algeria)

  • Nadia Mezouar

    (Faculty of Economies Sciences, Mascara University, Mascara 29000, Algeria)

  • Fatna Bensaber

    (Statistic and Random Modelization Laboratory, Tlemcen 13000, Algeria)

  • Salah Boulaaras

    (Department of Mathematics, College of Sciences and Arts in ArRass, Qassim University, Buraydah 51452, 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)

Abstract

In this work, by the use of a semigroup theory approach, we provide a global solution for an initial boundary value problem of the wave equation with logarithmic nonlinear source terms and fractional boundary dissipation. In addition to this, we establish a blow-up result for the solution under the condition of non-positive initial energy.

Suggested Citation

  • Amina Benramdane & Nadia Mezouar & Fatna Bensaber & Salah Boulaaras & Rashid Jan, 2023. "Blow-Up of Solution of Lamé Wave Equation with Fractional Damping and Logarithmic Nonlinearity Source Terms," Mathematics, MDPI, vol. 11(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4591-:d:1277021
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    References listed on IDEAS

    as
    1. Yuncheng You, 1996. "Inertial manifolds and stabilization of nonlinear beam equations with Balakrishnan-Taylor damping," Abstract and Applied Analysis, Hindawi, vol. 1, pages 1-20, January.
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