# Boundary conditions

From AMS Glossary

## boundary conditions

A set of mathematical conditions to be satisfied, in the solution of a differential equation, at the edges or physical boundaries (including fluid boundaries) of the region in which the solution is sought.

The nature of these conditions is usually determined by the physical nature of the problem, and is a necessary part of the problem's complete formulation. Common boundary conditions for the atmosphere are that the velocity component normal to the earth's surface vanish, and that the individual derivative of pressure vanish at the upper surface. The term is also used in the context of the time evolution of an "open" dynamical system that interacts with other "external" systems. The state of the external systems must be specified as a boundary condition to infer the evolution of the dynamical system under consideration. For example, the evolution of the earth's atmospheric state requires the specification of sea surface temperature as a boundary condition.

*See*kinematic boundary condition, dynamic boundary condition, boundary-value problem, initial condition.