2019/03/15 by Rinaldo M. Colombo, Colombo, Rinaldo, Vincent Perrollaz +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1903.06448
openalex publication_date 2019/03/15 · openalex created_date 2019/03/22 · openalex updated_date 2026/07/28
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.