Ammar, KaoutherWittbold, PetraCarrillo Menéndez, José2023-06-202023-06-2020060022-039610.1016/j.jde.2006.05.002https://hdl.handle.net/20.500.14352/49992We introduce a notion of entropy solution for a scalar conservation law on a bounded domain with nonhomogeneous boundary condition: u(t) + div Phi (u) = f on Q = (0, T) x Omega, u (0, (.))= u(0) on Q and "u = a on some part of the boundary (0, T) x partial derivative Omega." Existence and uniqueness of the entropy solution is established for any Phi is an element of C(R; R-N), u(0) is an element of L-infinity(Q), f is an element of L-infinity(Q), a is an element of L-infinity((0, T) x partial derivative Omega). In the L-1-setting, a corresponding result is proved for the more general notion of renormalised entropy solution.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S002203960600204Xhttp://www.sciencedirect.com/restricted access517.9Conservation lawNonhomogeneous boundary conditionsContinuous fluxPenalizationL1-TheoryRenormalized entropy solutionEcuaciones diferenciales1202.07 Ecuaciones en Diferencias