Some simple problems for the next generations

TL;DR

This paper presents a collection of open problems related to the global behavior over time of evolution systems governed by PDEs, highlighting their historical context and the challenges involved.

Contribution

It introduces a set of longstanding open problems in PDE evolution systems, providing background and partial results to guide future research.

Findings

List of open problems in PDE evolution systems

Partial results and background information provided

Highlights of difficulties in solving these problems

Abstract

A list of open problems on global behavior in time of some evolution systems, mainly governed by P.D.E, is given together with some background information explaining the context in which these problems appeared. The common characteristic of these problems is that they appeared a long time ago in the personnal research of the author and received almost no answer till then at the exception of very partial results which are listed to help the readers' understanding of the difficulties involved.