, Volume 107, Issue 2, pp 181-193

Measure-valued solutions of scalar conservation laws with boundary conditions

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Abstract

We define a solution concept for measure-valued solutions to scalar conservation laws with initial conditions and boundary conditions and prove a uniqueness theorem for such solutions. This result may be used to prove convergence, towards the unique solution, for approximate solutions which are uniformly bounded in L , weakly consistent with certain entropy inequalities and strongly consistent with the initial condition, i.e. without using derivative estimates. As an example convergence of a finite element method is demonstrated.

Communicated by L. Arkeryd