## Specify Boundary Conditions in the PDE Modeler App

Select **Boundary Mode** from the **Boundary**
menu or click the button. Then select a boundary or multiple boundaries for which you are
specifying the conditions. Note that no if you do not select any boundaries, then the
specified conditions apply to all boundaries.

To select a single boundary, click it using the left mouse button.

To select several boundaries and to deselect them, use

**Shift**+click (or click using the middle mouse button).To select all boundaries, use the

**Select All**option from the**Edit**menu.

Select **Specify Boundary Conditions** from
the **Boundary** menu.

**Specify Boundary Conditions** opens
a dialog box where you can specify the boundary condition for the
selected boundary segments. There are three different condition types:

Generalized Neumann conditions, where the boundary condition is determined by the coefficients

`q`

and`g`

according to the following equation:$$\overrightarrow{n}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\left(c\nabla u\right)+qu=g.$$

In the system cases,

`q`

is a 2-by-2 matrix and`g`

is a 2-by-1 vector.Dirichlet conditions:

*u*is specified on the boundary. The boundary condition equation is*hu*=*r*, where*h*is a weight factor that can be applied (normally 1).In the system cases,

`h`

is a 2-by-2 matrix and`r`

is a 2-by-1 vector.Mixed boundary conditions (system cases only), which is a mix of Dirichlet and Neumann conditions.

`q`

is a 2-by-2 matrix,`g`

is a 2-by-1 vector,`h`

is a 1-by-2 vector, and`r`

is a scalar.

The following figure shows the dialog box for the generic system
PDE (**Options > Application > Generic System**).

For boundary condition entries you can use the following variables
in a valid MATLAB^{®} expression:

The 2-D coordinates

`x`

and`y`

.A boundary segment parameter

`s`

, proportional to arc length.`s`

is 0 at the start of the boundary segment and increases to 1 along the boundary segment in the direction indicated by the arrow.The outward normal vector components

`nx`

and`ny`

. If you need the tangential vector, it can be expressed using`nx`

and`ny`

since*t*=_{x}*–n*and_{y}*t*=_{y}*n*._{x}The solution

`u`

.The time

`t`

.

**Note**

If the boundary condition is a function of the solution `u`

, you must
use the nonlinear solver. If the boundary condition is a function of the time
*t*, you must choose a parabolic or hyperbolic PDE.

Examples: `(100-80*s).*nx`

, and `cos(x.^2)`

In the nongeneric application modes, the **Description** column
contains descriptions of the physical interpretation of the boundary
condition parameters.