An algebraic approach for solving fourth-order partial differential equations

zbMATH Open1438.32033arXiv1907.08869MaRDI QIDQ4973706

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Publication date: 5 December 2019

Abstract: It is well-known that any solution of the Laplace equation is a real or imaginary part of a complex holomorphic function. In this paper, in some sense, we extend this property into four order hyperbolic and elliptic type PDEs. To be more specific, the extension is for a $c$-biwave PDE with constant coefficients, and we show that the components of a differentiable function on the associated hypercomplex algebras provide solutions for the equation.

Full work available at URL: https://arxiv.org/abs/1907.08869

zbMATH Keywords

partial differential equationscommutative algebramonogenic functionbiwave equation

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Representations of solutions to partial differential equations (35C99) Other partial differential equations of complex analysis in several variables (32W50)

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