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Peer-reviewedCC BY-NC-SA 4.0Asymptotic Analysis

NESTED DISCONTINUOUS ASYMPTOTIC PROFILES FOR THE VISCOUS BURGERS EQUATION WITH INFINITE MASS

  • Nicola de Nitti
  • Eliot Pacherie
Open at sourcePDFDOICite

Abstract

We study the viscous Burgers equation with a family of initial data having infinite mass. After rescaling, the solution converges toward a bounded discontinuous profile in the long-time limit. Moreover, by changing the scale near the discontinuity point again, we find a new profile that is also discontinuous. This process can be repeated an arbitrary number of times.

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Cite

BibTeXRIS
BibTeX
@article{nitti2026nested,
  title = {{NESTED DISCONTINUOUS ASYMPTOTIC PROFILES FOR THE VISCOUS BURGERS EQUATION WITH INFINITE MASS}},
  author = {Nicola de Nitti and Eliot Pacherie},
  journal = {Asymptotic Analysis},
  year = {2026},
  month = aug,
  doi = {10.1177/09217134261469833},
  eprint = {2406.10874},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05764049v1},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - JOUR
TI  - NESTED DISCONTINUOUS ASYMPTOTIC PROFILES FOR THE VISCOUS BURGERS EQUATION WITH INFINITE MASS
AU  - Nicola de Nitti
AU  - Eliot Pacherie
PY  - 2026
DA  - 2026/08/01
JO  - Asymptotic Analysis
DO  - 10.1177/09217134261469833
UR  - https://hal.science/hal-05764049v1
AB  - We study the viscous Burgers equation with a family of initial data having infinite mass. After rescaling, the solution converges toward a bounded discontinuous profile in the long-time limit. Moreover, by changing the scale near the discontinuity point again, we find a new profile that is also discontinuous. This process can be repeated an arbitrary number of times.
SN  - 0921-7134
SN  - 1875-8576
ER  -