From mintOC
Revision as of 17:21, 24 February 2016 by FelixMueller (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

This category contains all control problems which are governed by a parabolic partial differential equation.

A second order linear partial differential equation can be written as \sum^n_{i,j=1} a_{ij} \frac{\partial^2u}{\partial x_i \partial x_j} +\, \text{lower-order terms} = 0.

If the matrix A=(a_{ij})_{ij} is positive or negative semidefinite with exact one eigenvalue zero, the partial differential equation is called parabolic.

An example is the heat equation: \frac{\partial u}{\partial t}-\Delta u = f, where \Delta denotes the Laplace operator, u is the unknown, and the function f is given.

Pages in category "Parabolic"

This category contains only the following page.