Parabolic partial differential equation

From Wikipedia, the free encyclopedia

You have new messages (last change).

A parabolic partial differential equation is a second-order partial differential equation of the form

Au_{xx} + 2Bu_{xy} + Cu_{yy} + Du_{x} + Eu_{y} + F = 0 \quad

in which the matrix Z=\begin{bmatrix}A&B\\B&C\end{bmatrix} has the determinant equal to 0.

Some examples of parabolic partial differential equations are Schrödinger's equation and the heat equation. Physically, as in the heat equation, this corresponds to instant propagation of changes in u across the domain, but slow response to that change.

[edit] See also

 This mathematics-related article is a stub. You can help Wikipedia by expanding it.
Retrieved from "http://en.wikipedia.org../../../p/a/r/Parabolic_partial_differential_equation.html"
In other languages