## Documentation |

Elliptic and parabolic equations are used for modeling:

Steady and unsteady heat transfer in solids

Flows in porous media and diffusion problems

Electrostatics of dielectric and conductive media

Potential flow

Steady state of wave equations

Hyperbolic equation is used for:

Transient and harmonic wave propagation in acoustics and electromagnetics

Transverse motions of membranes

Eigenvalue problems are used for:

Determining natural vibration states in membranes and structural mechanics problems

In addition to solving generic scalar PDEs and generic systems
of PDEs with vector valued *u*, Partial Differential Equation Toolbox™ provides
tools for solving PDEs that occur in these common applications in
engineering and science:

The PDE app lets you specify PDE coefficients and boundary conditions in terms of physical entities. For example, you can specify Young's modulus in structural mechanics problems.

The application mode can be selected directly from the pop-up
menu in the upper right part of the PDE app or by selecting an application
from the **Application** submenu in the **Options** menu.
Changing the application resets all PDE coefficients and boundary
conditions to the default values for that specific application mode.

When using an application mode, the generic PDE coefficients
are replaced by application-specific parameters such as Young's modulus
for problems in structural mechanics. The application-specific parameters
are entered by selecting **Parameters** from
the **PDE** menu or by clicking the **PDE** button.
You can also access the PDE parameters by double-clicking a subdomain,
if you are in the PDE mode. That way it is possible to define PDE
parameters for problems with regions of different material properties.
The Boundary condition dialog box is also altered so that the Description
column reflects the physical meaning of the different boundary condition
coefficients. Finally, the Plot Selection dialog box allows you to
visualize the relevant physical variables for the selected application.

The PDE app lets you solve problems with vector valued *u* of
dimension two. However, you can use functions to solve problems for
any dimension of *u*.

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