English

Initial Data Identification in Conservation Laws and Hamilton-Jacobi Equations

Analysis of PDEs 2019-03-18 v1 Optimization and Control

Abstract

In the scalar 1D case, conservation laws and Hamilton-Jacobi equations are deeply related. For both, we characterize those profiles that can be attained as solutions at a given positive time corresponding to at least one initial datum. Then, for each of the two equations, we precisely identify all those initial data yielding a solution that coincide with a given profile at that positive time. Various topological and geometrical properties of the set of these initial data are then proved. 2000 Mathematics Subject Classification: 35L65, 35F21, 93B30, 35R30.

Keywords

Cite

@article{arxiv.1903.06448,
  title  = {Initial Data Identification in Conservation Laws and Hamilton-Jacobi Equations},
  author = {Rinaldo Colombo and Vincent Perrollaz},
  journal= {arXiv preprint arXiv:1903.06448},
  year   = {2019}
}
R2 v1 2026-06-23T08:09:09.123Z