A survey of functional and $L^p$ dissipativity theory

TL;DR

This survey reviews different notions of dissipativity for partial differential operators, focusing on functional and $L^p$-dissipativity, highlighting the authors' contributions to the field.

Contribution

The paper provides a comprehensive survey of dissipativity concepts for PDEs, emphasizing the authors' original results in the area.

Findings

Overview of various dissipativity notions for PDEs

Detailed discussion of $L^p$-dissipativity

Authors' original results on dissipativity theory

Abstract

Various notions of dissipativity type for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case $L^p$-dissipativity. Most of the results are due to the authors.