For example when a vibrating string is modelled, we assume that the two ends are held fixed: this accords with physical intuition. With the function to be found representing the displacement as function of position on the string, this implies the solution should take the value 0 at two points through all time.

The general picture is of a boundary (in one or several parts) where solutions are specified.

Famous in potential theory (an *elliptic* PDE) are the Dirichlet and Neumann boundary conditions, on a boundary enclosing a compact region. For a wave (*hyperbolic*) PDE one assumes waves propagate from an *initial disturbance* along some surface.

There are very many types of possible conditions.

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