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

## TL;DR

This paper investigates how singularities develop from initial data in Hamilton-Jacobi equations, providing conditions based on the initial data's subdifferential for the existence of singular characteristics at the initial time.

## Contribution

It offers new criteria linking the initial data's subdifferential properties to the generation of singularities in Hamilton-Jacobi solutions.

## Key findings

- Conditions for singularity generation depend on the proximal subdifferential of initial data.
- Existence of singular generalized characteristics is characterized at initial time.
- Results apply to a class of evolution Hamilton-Jacobi equations.

## Abstract

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