Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Discriminant of a PDE

  1. Feb 19, 2006 #1
    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?

    Last edited: Feb 19, 2006
  2. jcsd
  3. Feb 19, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    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".
  4. Feb 22, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    And, in fact, there are entire books written on "Hyperbolic-Elliptic" equations, "Parabolic-Elliptic" equations, etc.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Discriminant of a PDE
  1. Prerequisites for PDE ? (Replies: 10)

  2. Solutions to this PDE? (Replies: 4)

  3. Tough pde (Replies: 21)

  4. Linearity of PDE (Replies: 4)