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PreprintCC BY-NC-ND 4.0arXiv

Degenerated scalar balance laws: stability of the critical wave

  • Louis Garénaux
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Abstract

We consider scalar balance laws whith degenerated growth function at one infinity. It is the transition point between monostable and bistable waves. We find it admits smooth profiles arising from both settings, and show stability for the slowest of these waves, under a sign assumption on the flux. The presence of a characteristic point at infinity weaken the temporal decay: an exponential spatial localization loss is necessary to get algebraic temporal decay.

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Cite

BibTeXRIS
BibTeX
@misc{garenaux2026degenerated,
  title = {{Degenerated scalar balance laws: stability of the critical wave}},
  author = {Louis Garénaux},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23115},
  eprint = {2610.23115},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23115},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Degenerated scalar balance laws: stability of the critical wave
AU  - Louis Garénaux
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23115
UR  - https://arxiv.org/abs/2610.23115
AB  - We consider scalar balance laws whith degenerated growth function at one infinity. It is the transition point between monostable and bistable waves. We find it admits smooth profiles arising from both settings, and show stability for the slowest of these waves, under a sign assumption on the flux. The presence of a characteristic point at infinity weaken the temporal decay: an exponential spatial localization loss is necessary to get algebraic temporal decay.
ER  -