Category:Hyperbolic - Revision history

FelixMueller at 15:24, 24 February 2016

2016-02-24T15:24:19Z

← Older revision		Revision as of 15:24, 24 February 2016
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	This category contains all control problems which are governed by a hyperbolic partial differential equation.		This category contains all control problems which are governed by a hyperbolic partial differential equation.

			<p>
			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} +\, \text{lower-order terms} = 0</math>.
			</p>

			<p>
			If the matrix <math>A=(a_{ij})_{ij}</math> is indefinite such that <math>n-1</math> eigenvalues have the same sign and the remaining eigenvalue has the other sign, the partial differential equation is called hyperbolic.
			</p>
	<p>		<p>
	~~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>.~~

	If <math>A=(a_{ij})_{ij}</math> is indefinite such that <math>n-1</math> eigenvalues have the same sign and the remaining eigenvalue the other sign, the partial differential equation is called hyperbolic.

	An example is the wave equation: <math>\frac{\partial^2 u}{\partial t^2}-\Delta u = f</math>,		An example is the wave equation: <math>\frac{\partial^2 u}{\partial t^2}-\Delta u = f</math>,
	where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> is given.		where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> is given.
	</p>		</p>

	<!--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 -->		<!--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 -->

FelixMueller at 14:33, 24 February 2016

2016-02-24T14:33:42Z

← Older revision		Revision as of 14:33, 24 February 2016
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	An example is the wave equation: <math>\frac{\partial^2 u}{\partial t^2}-\Delta u = f</math>,		An example is the wave equation: <math>\frac{\partial^2 u}{\partial t^2}-\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.		where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> is given.
	</p>		</p>

FelixMueller at 14:29, 24 February 2016

2016-02-24T14:29:32Z

← Older revision		Revision as of 14:29, 24 February 2016
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	This category contains all control problems which are governed by a hyperbolic partial differential equation.		This category contains all control problems which are governed by a hyperbolic partial differential equation.
			<p>
			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>.

			If <math>A=(a_{ij})_{ij}</math> is indefinite such that <math>n-1</math> eigenvalues have the same sign and the remaining eigenvalue the other sign, the partial differential equation is called hyperbolic.

			An example is the wave equation: <math>\frac{\partial^2 u}{\partial t^2}-\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.
			</p>

	<!--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 -->		<!--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 -->

FelixMueller at 13:56, 23 February 2016

2016-02-23T13:56:42Z

← Older revision		Revision as of 13:56, 23 February 2016
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	[[Category: Model characterization]] [[Category: PDE model]]		<!--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 -->

			[[Category: Model characterization]]
			[[Category: PDE model]]

FelixMueller: Created page with "This category contains all control problems which are governed by a hyperbolic partial differential equation. Category: Model characterization Category: PDE model"

2016-02-23T12:19:48Z

Created page with "This category contains all control problems which are governed by a hyperbolic partial differential equation. Category: Model characterization Category: PDE model"

New page

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

[[Category: Model characterization]] [[Category: PDE model]]