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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Md. Asaduzzaman & Adem Kilicman & Md. Zulfikar Ali & Siti Hasana Sapar, 2020. "Fixed Point Theorem Based Solvability of 2-Dimensional Dissipative Cubic Nonlinear Klein-Gordon Equation," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1103-:d:380615
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    References listed on IDEAS

    as
    1. Wazwaz, Abdul-Majid, 2006. "Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1005-1013.
    2. Dong-mei Huang & Guo-liang Zou & L. W. Zhang, 2015. "Numerical Approximation of Nonlinear Klein-Gordon Equation Using an Element-Free Approach," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-11, October.
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