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There are many kinds of possible conditions, depending on the formulation of the problem, number of variables involved, and (crucially) the mathematical nature of the equation. Conditions imposed at a time ''t'' = 0 are called ''initial conditions''. One may also impose limiting conditions, for example under the limit of time ''t'' → +∞. Conditions in problems with a physical science origin usually match what is expected to determine a unique, well-defined physical situation. For example when a vibrating —a string held fixed at one end, with the other end free to vibrate. Physical analysis of the loose end implies that the appropriate boundary condition is that the solution's Derivative at this end is equal to 0 all time. The general picture is of a Boundary (in one or several parts) where solutions are specified. For partial differential equations boundary conditions are usually defined on a continuous Perimeter or Surface , rather than at discrete points. Famous in Potential Theory (typical of Elliptic PDE s) are the Dirichlet and Neumann Boundary Condition s, on a boundary enclosing a Compact region. For a Wave (''hyperbolic'') PDE one assumes waves propagate from an ''initial disturbance'' along some surface. SEE ALSO
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