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Well-posedness of general 1D Initial Boundary Value Problems for scalar balance laws

Elena Rossi 1
1 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its solutions with respect to variations in the flux and in the source terms. For both results, the initial and boundary data are required to be bounded functions with bounded total variation. The existence of solutions is obtained from the convergence of a Lax-Friedrichs type algorithm with operator splitting. The stability result follows from an application of Kružkov's doubling of variables technique, together with a careful treatment of the boundary terms.
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Submitted on : Monday, September 17, 2018 - 9:09:24 AM
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Elena Rossi. Well-posedness of general 1D Initial Boundary Value Problems for scalar balance laws. Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2019, 39 (6), pp.3577-3608. ⟨10.3934/dcds.2019147⟩. ⟨hal-01875159⟩

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