Construction of an infinite-dimensional family of exact solutions of a three-dimensional biharmonic equation by the hypercomplex method

TL;DR

This paper presents a novel hypercomplex method to construct an infinite-dimensional family of exact solutions for a three-dimensional biharmonic equation, advancing solution techniques for complex PDEs.

Contribution

It introduces a new hypercomplex approach to generate an infinite set of exact solutions for a specific class of three-dimensional biharmonic equations.

Findings

Successfully constructed an infinite-dimensional family of solutions

Demonstrated effectiveness of hypercomplex method for PDEs

Provides new tools for solving complex biharmonic equations

Abstract

An infinite-dimensional family of exact solutions of a three-dimensional biharmonic equation was constructed by the hypercomplex method.