Category:Elliptic: Difference between revisions

Revision as of 14:22, 24 February 2016

This category contains all control problems which are governed by an elliptic partial differential equation.

A second order linear partial differential equation can be written as

 $\sum_{i, j = 1}^{n} a_{i, j} \frac{\partial^{2}}{\partial x_{i} \partial x_{j}} + lower - orderterms = 0$ .

If  $A = (a_{i, j})_{i, j}$  is positive or negative definite, the partial differential equation is called elliptic.

An example is the Poisson's equation:  $- Δ u = f$ ,
where  $Δ$  denotes the Laplace operator,  $u$  is the unknown, and the function  $f$  given.

Pages in category "Elliptic"

The following 2 pages are in this category, out of 2 total.

C

Controlled Heating

S

Source Inversion

@@ Line 1: / Line 1: @@
 This category contains all control problems which are governed by an elliptic partial differential equation.
+A second order linear partial differential equation can be written as
+ <math>\sum^n_{i,j=1} a_{i,j} \frac{\partial^2}{\partial x_i \partial x_j} +\quad \textrm{ lower-order terms} = 0</math>.
+ If <math>A=(a_{i,j})_{i,j}</math> is positive or negative definite, the partial differential equation is called elliptic.
+ An example is the Poisson's equation: <math>-\Delta u = f</math>,
+ where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> given.