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

Mohamed Biomy, Khaled Zennir and Ahmed Himadan
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Mohamed Biomy: Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia
Khaled Zennir: Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia
Ahmed Himadan: Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia

Mathematics, 2020, vol. 8, issue 11, 1-21

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.

Keywords: nonlinear love-equation; local existence; global existence; infinite memory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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