Generation of singularities from the initial datum for Hamilton-Jacobi\n equations

2019/07/01 by Paolo G. Albano, Albano, Paolo, Piermarco Cannarsa +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1907.00796

openalex publication_date 2019/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the generation of singularities from the initial datum for a\nsolution of the Cauchy problem for a class of Hamilton-Jacobi equations of\nevolution. For such equations, we give conditions for the existence of singular\ngeneralized characteristics starting at the initial time from a given point of\nthe domain, depending on the properties of the proximal subdifferential of the\ninitial datum in a neighbourhood of that point.\n

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