The field equations of elasticity

[Trying2Learn]

TL;DR Summary

What is the mathematical category of the field equations of elasticity?

First, my ignorance... I know there are classes of equations: Laplace, Poisson, Wave, Diffusion, etc.

(I suppose Laplace is a subset of Poisson, but that is not the issue).

Into what category of mathematical equations would you place the field equations of elasticity (stress/strain/displacement)?

 

[Chestermiller]

Why do you feel that they need to have a specific name?

 

[Trying2Learn]

Why do you feel that they need to have a specific name?

Oh, I don't -- not in the least. Sometimes, names and categories undermine learning.

However, I DO know there are names given to the various types of differential equations and I am only interested to know if the field equations of elasticity are part of a particular category.

 

[pasmith]

The relevant categorisation is as elliptic (Poisson), parabolic (diffusion) or hyperbolic (wave).

The equation for displacement of an elastic medium has at leading order two time derivatives on the left and two space derivatives on the right, both with positive coefficieints; we have therefore a hyperbolic system.

 

[hunt_mat]

Are you talking about Navier's equations?

 

[Trying2Learn]

Yes to Mason and hunt

 

[Trying2Learn]

I think you are talking about Navier's equation. Am i right?

Yes