# Discriminant of a PDE

1. Feb 19, 2006

### Diophantus

A quick question:

When classifying a 2nd order PDE as either Hyperbolic, Parabolic or Elliptic we look at whether the discriminant is either positive, zero or negative respectively. Right. What do we do if the discriminant depends on independent variables (or the dependent variable for that matter) such that its sign can vary? Eg D = x. Do we classify it for the different values of x?

Regards.

Last edited: Feb 19, 2006
2. Feb 19, 2006

### saltydog

Yep, yep. Here's a quote:

"If the coefficients A, B, C are functions of x, y, and/or u (dep. variable), the equation may change from one classification to another at various points in the domain".

3. Feb 22, 2006

### HallsofIvy

Staff Emeritus
And, in fact, there are entire books written on "Hyperbolic-Elliptic" equations, "Parabolic-Elliptic" equations, etc.