L1 solutions to first order hyperbolic equations in bounded domains
Résumé
We consider L 1 solutions to the initial-boundary value problem for first order hyperbolic equations. We detail the interactions between the boundary condition and the flux function and the way they influence the integrability of the solution. Following (Bénilan P, Carrillo J, Wittbold P, Renormalized entropy solutions of scalar conservation laws. Ann Scuola Norm Sup Pisa Cl Sci 2000; 29(2):313–327.), we define a notion of renormalized entropy solution in order to ensure the integrability of the non-linear term in the entropy inequalities. Existence, uniqueness and stability of such a solution is established.