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An algebraic approach for solving fourth-order partial differential equation. (English) Zbl 1438.32033
Summary: 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.
32W50 Other partial differential equations of complex analysis in several variables
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
35C99 Representations of solutions to partial differential equations