EXISTENCE OF ENTROPY SOLUTIONS FOR MULTIDIMENSIONAL CONSERVATION LAWS WITH L 1 BOUNDARY CONDITIONS

Abstract : This paper deals with the construction of nonlinear boundary conditions for multidimensional conservation laws. Specifically by introducing a new type of entropy solution matching the boundary condition, the existence and uniqueness of a solution belonging to L ∞ ∩ BV is proved by using the Di Perna-Lions regularization method. The new entropy solution, which takes advantage by the entropy criterion introduced by Bardos-Le Roux-Nédélec for first-order quasilinear equations with boundary conditions, is based on a weaker assumption at the boundary.
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Christian Dogbe, C. Bianca. EXISTENCE OF ENTROPY SOLUTIONS FOR MULTIDIMENSIONAL CONSERVATION LAWS WITH L 1 BOUNDARY CONDITIONS. Mathematics in Engineering, Science and Aerospace (MESA) , 2018, Vol. 9 (No. 4), pp.507-526. ⟨hal-02151726⟩

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