Measurable process selection theorem and non-autonomous inclusions

TL;DR

This paper establishes a theoretical framework for the existence of measurable semi-processes in non-autonomous differential equations and inclusions, accommodating non-uniqueness and finite-time blow-up scenarios.

Contribution

It introduces a measurable process selection theorem for non-autonomous systems without uniqueness, including cases with finite-time blow-up.

Findings

Proves existence of measurable semi-processes under broad conditions

Handles non-uniqueness in non-autonomous differential inclusions

Allows for solutions that blow up in finite time

Abstract

A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in the situations where there is no uniqueness. Also, we allow solutions to blow up in finite time and then obtain local semi-processes.