# 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/)