  We introduce in this contribution the notion of partial Riemann problem.
Recall that the Riemann problem describes a shock tube interaction between two
given states ; the partial Riemann problem is a generalization of the previous
concept and introduces the notion of boundary manifold. In what follows, we
first recall very classical notions concerning gas dynamics and the associated
Riemann problem. In a second part, we introduce the partial Riemann problem for
general systems of conservation laws and proves that this problem admits a
solution in some class of appropriate nonlinear waves. In section 3, we recall
the linearized analysis with the method of characteristics, introduce the weak
formulation of the Dirichlet boundary condition for nonlinear situations in
terms of the partial Riemann problem and show that lot of physically relevant
situations are described with this theoretical framework. In the last
paragraph, we propose a practical implementation of the previous onsiderations
with the finite volume method.
