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Entropy solutions in $BV^s$ for a class of triangular systems involving a transport equation

Abstract : Strictly hyperbolic triangular systems with a decoupled nonlinear conservation law and a coupled ``linear'' transport equation with a discontinuous velocity are known to create measure solutions for the initial value problem. Adding a uniform strictly hyperbolic assumption on such systems we are able to obtain bounded solutions in $L^\infty$ under optimal fractional $BV$ regularity of the initial data. The Pressure Swing Adsorption process (PSA) [16] is an example coming from chemistry which, after a change of variables from Euler to Lagrange, has such a triangular structure. Here, we provide global weak $L^\infty$ entropy solutions in the framework of fractional $BV$ spaces: $BV^s$, $ 1/ 3 < s < 1$, when the zero set of the second derivative of the decoupled flux is locally finite. In addition, for some initial data not in $BV^{1/3}$, a blow-up in $L^\infty$ may occur.
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https://hal.archives-ouvertes.fr/hal-02895603
Contributor : Stéphane Junca <>
Submitted on : Thursday, July 9, 2020 - 8:31:35 PM
Last modification on : Monday, October 12, 2020 - 2:28:06 PM

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  • HAL Id : hal-02895603, version 1

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Christian Bourdarias, Anupam Pal Choudhury, Billel Guelmame, Stéphane Junca. Entropy solutions in $BV^s$ for a class of triangular systems involving a transport equation. 2020. ⟨hal-02895603⟩

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