Explore BrainMass

Diffusion Equations : Classify the PDE's as Elliptic, Parabolic or Hyperbolic

Classify the following PDE's as elliptic, parabolic or hyperbolic. If mixed, identify the regions and classify within each region.

(b) xuxx - uxy + yuxy +3uy = 1

Please see the attached file for the fully formatted problem.


Solution Preview

The most important thinf to recognize in determining this solution is how to look at the coefficients. In order to classify as on of these types we use the model:

B^2 -4AC

If this solution greater then zero then it is hyperbolic, if equal to zero then parabolic, if less then zero the elliptic.

The A,B,C terms represent coefficients in our PDE. The sign of these coefficient is what is most ...

Solution Summary

A PDE is clssified as elliptic, parabolic or hyperbolic.