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Article Dans Une Revue Journal of Hyperbolic Differential Equations Année : 2021

EXISTENCE AND UNIQUENESS OF GENERALIZED SOLUTIONS TO HYPERBOLIC SYSTEMS WITH LINEAR FLUXES AND STIFF SOURCES

Nina Aguillon
Bruno Després
Edwige Godlewski
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Michael Ndjinga

Résumé

Motivated by the modelling of boiling two-phase flows, we study systems of balance laws with a source term defined as a discontinuous function of the unknown. Due to this discontinuous source term, the classical theory of partial differential equations (PDE) is not sufficient here. Restricting to a simpler system with linear fluxes, a notion of generalized solution is developed. An important point in the construction of a solution is that the curve along which the source jumps, which we call the boiling curve, must never be tangent to the characteristics. This leads to exhibit sufficient conditions which ensure the existence and uniqueness of a solution in two different situations: first when the initial data is smooth and such that the boiling curve is either overcharacteristic or
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Dates et versions

hal-02920155 , version 1 (24-08-2020)

Identifiants

  • HAL Id : hal-02920155 , version 1

Citer

Teddy Pichard, Nina Aguillon, Bruno Després, Edwige Godlewski, Michael Ndjinga. EXISTENCE AND UNIQUENESS OF GENERALIZED SOLUTIONS TO HYPERBOLIC SYSTEMS WITH LINEAR FLUXES AND STIFF SOURCES. Journal of Hyperbolic Differential Equations, In press, 18 (3), https://doi.org/10.1142/S021989162150020X. ⟨hal-02920155⟩
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