On a Generalized Lam\'e-Navier system in $\mathbb{R}^3$

TL;DR

This paper generalizes the classical Lamé-Navier system in linear elasticity using Clifford algebra and Dirac operators, providing new theoretical insights and computational methods for solutions.

Contribution

It introduces a generalized Lamé-Navier system via Clifford algebra and Dirac operators, and develops algorithms for analyzing these systems.

Findings

Identification of structures in solutions of generalized systems

Development of MATLAB algorithms for PDE operators

Verification of theoretical results through computational experiments

Abstract

This paper is devoted to a fundamental system of equations in Linear Elasticity Theory: the famous Lam\'e-Navier system. The Clifford algebra language allows us to rewrite this system in terms of the euclidean Dirac operator, which at the same time suggests a very natural generalization involving the so-called structural sets. We are interested in finding some structures in the solutions of these generalized Lam\'e-Navier systems. Using MATLAB we also implement algorithms to compute with such partial differential operators as well as to verify some theoretical results obtained in the paper.