Difference between revisions of "Category:Parabolic"
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A second order linear partial differential equation can be written as | A second order linear partial differential equation can be written as | ||
| − | <math>\sum^n_{i,j=1} a_{ij} \frac{\partial^2u}{\partial x_i \partial x_j} +\quad \textrm{ lower-order terms} = 0</math>. | + | <math>\sum^n_{i,j=1} a_{ij} \frac{\partial^2u}{\partial x_i \partial x_j} +\quad \textrm{ lower-order terms} = 0</math>. </p |
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| + | <p> | ||
If <math>A=(a_{ij})_{ij}</math> is positive or negative semidefinite with exact one eigenvalue zero, the partial differential equation is called parabolic. | If <math>A=(a_{ij})_{ij}</math> is positive or negative semidefinite with exact one eigenvalue zero, the partial differential equation is called parabolic. | ||
Revision as of 16:19, 24 February 2016
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
. </p
<p>
If 
is positive or negative semidefinite with exact one eigenvalue zero, the partial differential equation is called parabolic.
An example is the heat equation: 
,
where 
denotes the Laplace operator, 
is the unknown, and the function 
is given.
Pages in category "Parabolic"
This category contains only the following page.
