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

Chalermpon Bunpog
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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

Mathematics, 2018, vol. 6, issue 7, 1-11

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.

Keywords: boundary value problem; Green’s identity; Green’s function; tempered distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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