Difference between revisions of "Category:Parabolic"
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| − | 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 the matrix <math>A=(a_{ij})_{ij}</math> is positive or negative semidefinite with exact one eigenvalue zero, the partial differential equation is called parabolic. |
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An example is the heat equation: <math>\frac{\partial u}{\partial t}-\Delta u = f</math>, | An example is the heat equation: <math>\frac{\partial u}{\partial t}-\Delta u = f</math>, | ||
Latest revision as of 16:21, 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
.
If the matrix 
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.
