English

Nested discontinuous asymptotic profiles for the viscous Burgers equation with infinite mass

Analysis of PDEs 2024-06-18 v1

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.

Keywords

Cite

@article{arxiv.2406.10874,
  title  = {Nested discontinuous asymptotic profiles for the viscous Burgers equation with infinite mass},
  author = {Nicola de Nitti and Eliot Pacherie},
  journal= {arXiv preprint arXiv:2406.10874},
  year   = {2024}
}