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General Decay Rate of Solution for Love-Equation with Past History and Absorption

Author

Listed:
  • 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, Algeria)

  • Mohamad 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)

Abstract

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, a new class of nonlinear Love-equation with infinite memory in the presence of source term that takes general nonlinearity form. New minimal conditions on the relaxation function and the relationship between the weights of source term are used to show a very general decay rate for solution by certain properties of convex functions combined with some estimates. Investigations on the propagation of surface waves of Love-type have been made by many authors in different models and many attempts to solve Love’s equation have been performed, in view of its wide applicability. To our knowledge, there are no decay results for damped equations of Love waves or Love type waves. However, the existence of solution or blow up results, with different boundary conditions, have been extensively studied by many authors. Our interest in this paper arose in the first place in consequence of a query for a new decay rate, which is related to those for infinite memory ϖ in the third section. We found that the system energy decreased according to a very general rate that includes all previous results.

Suggested Citation

  • Khaled Zennir & Mohamad Biomy, 2020. "General Decay Rate of Solution for Love-Equation with Past History and Absorption," Mathematics, MDPI, vol. 8(9), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1632-:d:416652
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