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Local and Global Existence of Solution for Love Type Waves with Past History

Author

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  • Mohamed Biomy

    (Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia
    Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said 42511, Egypt)

  • Khaled Zennir

    (Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia
    Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma. B.P. 401, Guelma 24000, Algerie)

  • Ahmed Himadan

    (Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia)

Abstract

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

Suggested Citation

  • Mohamed Biomy & Khaled Zennir & Ahmed Himadan, 2020. "Local and Global Existence of Solution for Love Type Waves with Past History," Mathematics, MDPI, vol. 8(11), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1998-:d:442052
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    References listed on IDEAS

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    1. S. C. Oukouomi Noutchie & E. F. Doungmo Goufo, 2014. "Exact Solutions of Fragmentation Equations with General Fragmentation Rates and Separable Particles Distribution Kernels," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-5, July.
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