The mathematical model for a physical process is usually a partial differential or an ordinary differential equation prescribed over a physical domain, which has boundaries. The behaviour of the function representing the physical process needs to be defined on the boundaries, and these are the boundary conditions. For example, the flow around a body translating at constant speed
in an ideal incompressible fluid. The velocity field of the flow is given as the gradient of a potential function
,
which satisfies the Laplace's equation
and has to satisfy the kinematic boundary condition
If the fluid domain is unbounded, we need to specify the behavior of
as
,
which is
Timothy S Choe
2003-03-15