Hypercomplex monogenic functions of the biharmonic variable in some problems of plane elasticity theory

1Gryshchuk, SV
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2015, 6:7-12
https://doi.org/10.15407/dopovidi2015.06.007
Section: Mathematics
Language: Ukrainian
Abstract: 

Solutions of the Lamè equilibrium system of equations for displacements are obtained via components of the hypercomplex monogenic functions of the biharmonic variable. The description of all monogenic functions, for which one of the real components is a biharmonic function associated with a solution of the Flamant problem for an isotropic half-plane, is obtained.

Keywords: biharmonic algebra, biharmonic equation, biharmonic function, biharmonic plane, Flamant problem for isotropic semiplane, Lamè equilibrium system in displacements, monogenic function
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