An algebraic approach for solving fourth-order partial differential equations
Analysis of PDEs
2019-07-23 v1
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 -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.
Cite
@article{arxiv.1907.08869,
title = {An algebraic approach for solving fourth-order partial differential equations},
author = {A. Pogorui and T. Kolomiiets and R. M. Rodriguez-Dagnino},
journal= {arXiv preprint arXiv:1907.08869},
year = {2019}
}