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 Kruzkov's doubling of variables technique, together with a careful treatment of the boundary terms.

Rossi, E. (2019). Well-posedness of general 1d initial boundary value problems for scalar balance laws. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 39(6), 3577-3608 [10.3934/dcds.2019147].

Well-posedness of general 1d initial boundary value problems for scalar balance laws

Rossi, Elena
2019

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 Kruzkov's doubling of variables technique, together with a careful treatment of the boundary terms.
Articolo in rivista - Articolo scientifico
Balance laws; Initial-boundary value problem; Lax-friedrichs scheme; Stability estimates; Well-posedness
English
2019
39
6
3577
3608
none
Rossi, E. (2019). Well-posedness of general 1d initial boundary value problems for scalar balance laws. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 39(6), 3577-3608 [10.3934/dcds.2019147].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/229584
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