New interaction estimates for the Baiti-Jenssen system

Laura  Caravenna; Laura V.  Spinolo; Laura  Caravenna; Laura V.  Spinolo

doi:10.3934/nhm.2016.11.263

Networks and Heterogeneous Media

2016, Volume 11, Issue 2: 263-280. doi: 10.3934/nhm.2016.11.263

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New interaction estimates for the Baiti-Jenssen system

Laura Caravenna ^{1
,},
Laura V. Spinolo ^{2
,}

1.
Dipartimento di Matematica, Università degli Studi di Padova, via Trieste 63, 35121 Padova
2.
IMATI-CNR, via Ferrata 1, 27100 Pavia

Received: 01 April 2015 Revised: 01 October 2015
Primary: 35L65; Secondary: 35L67.

We establish new interaction estimates for a system introduced by Baiti and Jenssen. These estimates are pivotal to the analysis of the wave front-tracking approximation. In a companion paper we use them to construct a counter-example which shows that Schaeffer's Regularity Theorem for scalar conservation laws does not extend to systems. The counter-example we construct shows, furthermore, that a wave-pattern containing infinitely many shocks can be robust with respect to perturbations of the initial data. The proof of the interaction estimates is based on the explicit computation of the wave fan curves and on a perturbation argument.
- Conservation laws,
- regularity,
- shock formation,
- Schaeffer theorem,
- counter-example
Citation: Laura Caravenna, Laura V. Spinolo. New interaction estimates for the Baiti-Jenssen system[J]. Networks and Heterogeneous Media, 2016, 11(2): 263-280. doi: 10.3934/nhm.2016.11.263

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Abstract

We establish new interaction estimates for a system introduced by Baiti and Jenssen. These estimates are pivotal to the analysis of the wave front-tracking approximation. In a companion paper we use them to construct a counter-example which shows that Schaeffer's Regularity Theorem for scalar conservation laws does not extend to systems. The counter-example we construct shows, furthermore, that a wave-pattern containing infinitely many shocks can be robust with respect to perturbations of the initial data. The proof of the interaction estimates is based on the explicit computation of the wave fan curves and on a perturbation argument.

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