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.
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}
}