Category:Elliptic - Revision history

FelixMueller at 15:22, 24 February 2016

2016-02-24T15:22:55Z

← Older revision		Revision as of 15:22, 24 February 2016
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	This category contains all control problems which are governed by an elliptic partial differential equation.		This category contains all control problems which are governed by an elliptic partial differential equation.

	<p>		<p>
	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^~~2 u~~}{\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} +\, \text{lower-order terms} = 0</math>.
			</p>
	If <math>A=(a_{ij})_{ij}</math> is positive or negative definite, the partial differential equation is called elliptic.
			<p>
	An example is the Poisson's equation: <math>-\Delta u = f</math>,		If the matrix <math>A=(a_{ij})_{ij}</math> is positive or negative definite, the partial differential equation is called elliptic.
			</p>
			<p>
			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> 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>

2016-02-24T14:33:14Z

← Older revision		Revision as of 14:33, 24 February 2016
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	An example is the Poisson's equation: <math>-\Delta u = f</math>,		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.		where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> is given.
	</p>		</p>

2016-02-24T14:26:16Z

← Older revision		Revision as of 14:26, 24 February 2016
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	<p>		<p>
	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_{~~i,j~~} \frac{\partial^2}{\partial x_i \partial x_j} +\quad \textrm{ lower-order terms} = 0</math>.		<math>\sum^n_{i,j=1} a_{ij} \frac{\partial^2 u}{\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.		If <math>A=(a_{ij})_{ij}</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>,		An example is the Poisson's equation: <math>-\Delta u = f</math>,

2016-02-24T14:23:08Z

← Older revision		Revision as of 14:23, 24 February 2016
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	This category contains all control problems which are governed by an elliptic partial differential equation.		This category contains all control problems which are governed by an elliptic partial differential equation.
			<p>
	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_{i,j} \frac{\partial^2}{\partial x_i \partial x_j} +\quad \textrm{ lower-order terms} = 0</math>.		<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>.
Line 8:		Line 8:
	An example is the Poisson's equation: <math>-\Delta u = f</math>,		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.		where <math>\Delta</math> denotes the Laplace operator, <math>u</math> is the unknown, and the function <math>f</math> given.
			</p>

2016-02-24T14:22:17Z

← Older revision		Revision as of 14:22, 24 February 2016
Line 1:		Line 1:
	This category contains all control problems which are governed by an elliptic partial differential equation.		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.

2016-02-23T13:56:35Z

← Older revision		Revision as of 13:56, 23 February 2016
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	This category contains all control problems which are governed by an elliptic partial differential equation.		This category contains all control problems which are governed by an elliptic partial differential equation.

	[[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]]

2016-02-23T12:20:09Z

← Older revision		Revision as of 12:20, 23 February 2016
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	This category contains all control problems which are governed by an elliptic partial differential equation.		This category contains all control problems which are governed by an elliptic partial differential equation.

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

2016-02-23T12:18:50Z

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

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