Difference between revisions of "Category:Parabolic"

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This category contains all control problems which are governed by a parabolic partial differential equation.
 
This category contains all control problems which are governed by a parabolic partial differential equation.
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<p>
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A second order linear partial differential equation can be written as
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<math>\sum^n_{i,j=1} a_{ij} \frac{\partial^2u}{\partial x_i \partial x_j} +\, \text{lower-order terms} = 0</math>.
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</p>
  
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<p>
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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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</p>
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<p>
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An example is the heat equation: <math>\frac{\partial u}{\partial t}-\Delta u = f</math>,
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where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> is given.
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</p>
  
[[Category: Model characterization]] [[Category: PDE model]]
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<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->
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[[Category: Model characterization]]  
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[[Category: PDE model]]

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 \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.