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PreprintCC BY-SA 4.0HAL

Global boundary stabilization of 1d systems of scalar conservation laws

  • Georges Bastin
  • Jean-Michel Coron
  • Amaury Hayat
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Abstract

We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback control laws. Our first contribution establishes the well-posedness of the system in the space of L∞ entropy solutions. Our second contribution provides a set of sufficient dissipative conditions on the boundary coupling that ensure global exponential stability in L1 and L∞ norms.

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Cite

BibTeXRIS
BibTeX
@misc{bastin2026global,
  title = {{Global boundary stabilization of 1d systems of scalar conservation laws}},
  author = {Georges Bastin and Jean-Michel Coron and Amaury Hayat},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05581913v2},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Global boundary stabilization of 1d systems of scalar conservation laws
AU  - Georges Bastin
AU  - Jean-Michel Coron
AU  - Amaury Hayat
PY  - 2026
DA  - 2026/09/28
PB  - HAL
UR  - https://hal.science/hal-05581913v2
AB  - We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback control laws. Our first contribution establishes the well-posedness of the system in the space of L^∞ entropy solutions. Our second contribution provides a set of sufficient dissipative conditions on the boundary coupling that ensure global exponential stability in L^1 and L^∞ norms.
ER  -