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

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2020-07, Vol.8 (7), p.1103
Main Authors: Asaduzzaman, Md, Kilicman, Adem, Ali, Md. Zulfikar, Sapar, Siti Hasana
Format: Article
Language:English
Subjects:
2-Dimensional dissipative cubic nonlinear Klein-Gordon equation
Banach spaces
Estimates
Existence theorems
Fixed points (mathematics)
Galerkin method
GLK method
Inequality
Klein-Gordon equation
LS fixed point theorem
Mathematics
Ordinary differential equations
Partial differential equations
periodic solution
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8071103