# Scalar Kernels

-   Scalar Kernels:
    -   Operate on *scalar* variables (`family = SCALAR`).
    -   Are defined in the `[ScalarKernels]` section of your input file.
-   Use them for:
    -   Solving ODEs (see example 18).
    -   Formulations with Lagrange multipliers.
    -   Contact
    -   Other applications...
-   Notes:
    -   Mesh-specific data such as `qp` and `currentelem` are not available to `ScalarKernels`.

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-   Problem being solved:

$$$
\begin{aligned}
      \frac{\partial u}{\partial t} &= \nabla^2 u + f    && \text{in }\Omega = [-1, 1] \\
      u &= X(t) && \text{on }\Gamma_{\text{left}}\\
      u &= Y(t) && \text{on }\Gamma_{\text{right}}\\
\end{aligned}
$$$ 

-   Where the boundary conditions are governed by the ODEs:

$$$ 
\begin{aligned}
      \frac{dX}{dt} &= 3X + 2Y \\[6pt]
      \frac{dY}{dt} &= 4X +  Y \\
\end{aligned}
$$$ 
plus suitable initial conditions.

[Example 18](/wiki/MooseExamples/Example_18/)