# PoissonPDEComponent

PoissonPDEComponent[vars,pars]

yields a Poisson PDE term with model variables vars and model parameters pars.

# Details • PoissonPDEComponent returns a sum of differential operators to be used as a part of partial differential equations:
• • PoissonPDEComponent can be used to model Poisson equations with dependent variable , independent variables and time variable .
• Stationary model variables vars are vars={u[x1,,xn],{x1,,xn}}.
• Time-dependent model variables vars are vars={u[t,x1,,xn],t,{x1,,xn}}.
• The PoissonPDEComponent is based on a diffusion and source term:
• • The Poisson PDE term is realized as a DiffusionPDETerm with 1 as a diffusion coefficient and a SourcePDETerm with coefficient resulting in .
• The following model parameters pars can be given:
•  parameter default symbol "PoissonSourceTerm" 1 • The source term coefficient is a scalar.
• The source term coefficient can depend on time, space, parameters and the dependent variables.
• If the PoissonPDEComponent depends on parameters that are specified in the association pars as ,keypi,pivi,], the parameters are replaced with .

# Examples

## Basic Examples(4)

Define a Poisson PDE component:

Define a Poisson PDE component with a symbolic coefficient:

Find the eigenvalues of a Poisson PDE component:

Solve a Poisson equation:

Visualize the result: