Well Posed Problem

A well posed problem requires

1. Mathematical solution exists
2. The solution must be unique
3. the solution is stable

Example: consider the governing equations with constant transport properties and no radiation and heat source terms.

5 equations with 5 unknowns, then the solution exists, however it is not unique. Boundary conditions specified at two locations. Initial conditions specified at one instant t. Note the number of boundar conditions needed depends on the type of governing equation and the order of the partial differential equation. If a problem has a proper boundary and initial conditions then the solution will be unique.