Fixed Point Theorem Based Solvability of 2-Dimensional Dissipative Cubic Nonlinear Klein-Gordon Equation

Md. Asaduzzaman, Adem Kilicman, Md. Zulfikar Ali and Siti Hasana Sapar
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Md. Asaduzzaman: Department of Mathematics, Islamic University, Kushtia 7003, Bangladesh
Adem Kilicman: Institute for Mathematical Research, Department of Mathematics, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
Md. Zulfikar Ali: Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
Siti Hasana Sapar: Institute for Mathematical Research, Department of Mathematics, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia

Mathematics, 2020, vol. 8, issue 7, 1-12

Abstract: The purpose of this article is to establish the solvability of the 2-Dimensional dissipative cubic nonlinear Klein-Gordon equation (2DDCNLKGE) through periodic boundary value conditions (PBVCs). The analysis of this study is founded on the Galerkin’s method (GLK) and the Leray-Schauder’s fixed point theorem (LS). First, the GLK method is used to construct some uniform priori estimates of approximate solution to the corresponding equation of 2DDCNLKGE. Finally, the LS fixed point theorem is applied to obtain the efficient and straightforward existence and uniqueness criteria of time periodic solution to the 2DDCNLKGE.

Keywords: 2-Dimensional dissipative cubic nonlinear Klein-Gordon equation; periodic solution; GLK method; LS fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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