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This category contains all control problems which are governed by a hyperbolic partial differential equation.

A second order linear partial differential equation can be written as \sum^n_{i,j=1} a_{ij} \frac{\partial^2u}{\partial x_i \partial x_j} +\, \text{lower-order terms} = 0.

If the matrix A=(a_{ij})_{ij} is indefinite such that n-1 eigenvalues have the same sign and the remaining eigenvalue has the other sign, the partial differential equation is called hyperbolic.

An example is the wave equation: \frac{\partial^2 u}{\partial t^2}-\Delta u = f, where \Delta denotes the Laplace operator, u is the unknown, and the function f is given.

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