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Boundary Value Problem of the Operator ⊕ k Related to the Biharmonic Operator and the Diamond Operator

Author

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  • Chalermpon Bunpog

    (Center of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

This paper presents an alternative methodology for finding the solution of the boundary value problem (BVP) for the linear partial differential operator. We are particularly interested in the linear operator ⊕ k , where ⊕ k = ♡ k ♢ k , ♡ k is the biharmonic operator iterated k -times and ♢ k is the diamond operator iterated k -times. The solution is built on the Green’s identity of the operators ♡ k and ⊕ k , in which their derivations are also provided. To illustrate our findings, the example with prescribed boundary conditions is exhibited.

Suggested Citation

  • Chalermpon Bunpog, 2018. "Boundary Value Problem of the Operator ⊕ k Related to the Biharmonic Operator and the Diamond Operator," Mathematics, MDPI, vol. 6(7), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:7:p:115-:d:156353
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    References listed on IDEAS

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    1. A. Kananthai & S. Suantai, 2003. "On the convolution product of the distributional kernel K α , β , γ , ν," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-6, January.
    2. Amphon Liangprom & Kamsing Nonlaopon, 2011. "On the Convolution Equation Related to the Diamond Klein-Gordon Operator," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, October.
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    Cited by:

    1. Kamsing Nonlaopon, 2019. "On the Inverse Ultrahyperbolic Klein-Gordon Kernel," Mathematics, MDPI, vol. 7(6), pages 1-11, June.

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    1. Kamsing Nonlaopon, 2019. "On the Inverse Ultrahyperbolic Klein-Gordon Kernel," Mathematics, MDPI, vol. 7(6), pages 1-11, June.

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