This collection consists of selected scientific results stemming from the conference "Methusalem Workshop on Classical Analysis and PDEs", held at the Ghent University from 27th February 2023 to 1st March 2023. The workshop was organized by the "Ghent Analysis & PDE Center". The presented materials mainly consist of scientific results on classical analysis and problems of PDEs. In particular, results on harmonic analysis, functional spaces, functional inequalities, inverse problems, non-local PDEs, non-classical problems of PDEs, integro-differential equations, hypoelliptic operators, pseudo-differential calculus, and others are given.

Michael Ruzhansky is a Senior Full Professor of Mathematics at Ghent University in Belgium, and a Professor of Mathematics at Queen Mary University of London in the United Kingdom. His research interests mainly lie in Partial Differential Equations, Microlocal and Harmonic Analysis, and Pseudo-Differential Operators on Lie Groups and Manifolds. Previously, he had appointments at Utrecht University, Johns Hopkins University, University of Edinburgh, and Imperial College London. He is the recipient of various awards and fellowships, notably, the Ferran Sunyer i Balaguer Prize in 2014 and 2018, Daiwa Adrian Prize in 2010, and the ISAAC award in 2007. He is serving as the head of the Ghent Analysis & PDE Center of Ghent University. Berikbol Torebek is a Postdoctoral Researcher at the Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University in Belgium and Leading Researcher at the Institute of Mathematics and Mathematical Modeling in Kazakhstan. He is a member of the research group Analysis and PDEs led by Prof. Michael Ruzhansky. He obtained his PhD in Mathematics in July 2017 from the Al-Farabi Kazakh University. His research interests lie in classical and fractional Partial Differential Equations. In particular, he is interested in the solvability and qualitative properties of solutions to nonlinear problems. He is currently a member of the editorial boards of international journals "Fractional Differential Calculus", "International Journal of Mathematics and Physics" and "Kazakh Mathematical Journal".