Mathematics

Construction of polynomial solutions to the Dirichlet problem for the biharmonic equation in a ball

V. V. Karachik, N. A. Antropova

South Ural State University

Abstract: Polynomial solution to the Dirihlet problem for the nonhomogeneous biharmonic equation with polynomial right hand side and polynomial boundary data in a ball is constructed. Explicit representation of harmonic functions in the Almansi representation is used.

Keywords: biharmonic equation, polynomial solutions, Dirichlet problem, Almansi equation.

UDC: 517.956.225+517.575

Received: 01.10.2011

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