# ReactionPDETerm

ReactionPDETerm[vars,a]

represents a reaction term with reaction coefficient and with model variables vars.

ReactionPDETerm[{u,{x1,,xn}},a,pars]

uses model parameters pars.

# Details  • Reaction terms are used to model absorption or emission in a number of domains, such as biology, chemistry and physics.
• Reaction with a reaction coefficient is the process of absorbing of the dependent variable :
• • ReactionPDETerm returns differential operators term to be used as a part of partial differential equations:
• • ReactionPDETerm can be used to model reaction 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],{x1,,xn}} or vars={u[t,x1,,xn],t,{x1,,xn}}.
• The reaction term in context with other PDE terms is given by:
• • The reaction coefficient has the following form:
•  scalar a
• For a system of PDEs with dependent variables {u1,,um}, the reaction represents:
• • The reaction term in context systems of PDE terms:
• • The reaction coefficient is a tensor of rank 2 of the form where each submatrix is a scalar that can specified in the same way as for a single dependent variable.
• The reaction coefficient can depend on time, space, parameters and the dependent variables.
• The coefficient does not affect the meaning of NeumannValue.
• All quantities that do not explicitly depend on the independent variables given are taken to have zero partial derivative.

# Examples

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## Basic Examples(4)

Define a stationary reaction term:

Define a stationary reaction term with a parameter:

Solve a reaction diffusion equation build with basic terms:

Visualize the result:

Solve for the eigenvalues of a reaction diffusion equation:

## Scope(6)

Define a time-dependent reaction term:

Define a symbolic reaction term:

Define a 2D stationary reaction term:

Define a reaction term with multiple dependent variables:

Define a Helmholtz model:

Solve for the eigenvalues of the Helmholtz equation:

Solve the Helmholtz equation with a source term:

Visualize the solution:

Solve a nonlinear reaction diffusion equation build with basic terms:

Visualize the result: