Extended Abstracts MWCAPDE 2023, 1st ed. 2024
Methusalem Workshop on Classical Analysis and Partial Differential Equations
Research Perspectives Ghent Analysis and PDE Center Series

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.

Preface.- I. Theory of Functional Analysis, Operator Theory, and Applications.- Elena Afanaseva, Anatoly Golberg: Mappings of finite area distortion: Hausdorff measures.- Alexander Cardona, Santiago Gomez Cobos: The principal symbol of elliptic differential operators on Lie groups and homogeneous spaces.- Arran Fernandez, Cihan Gueder, Walaa Yasin: On fractional quaternionic d-bar derivatives.- Brian Grajales, Julieth Saavedra: A note on homogeneous geometry of G2-type real flag manifolds.- Junqing Huang: Semi-sparsity for Piecewise Constant Functions on Triangular Mesh Denoising.- Mikhail Isaev, Roman G. Novikov, Grigory V. Sabinin: Superresolution reconstruction from truncated Fourier transform.- Aitolkyn H. Kalidolday, Erlan D. Nursultanov: Interpolation theorem for discrete net spaces.- Vishvesh Kumar, Joel E. Restrepo: Titchmarsh theorem by modulus of continuity for the deformed Hankel–Lipschitz classes.- Juan Pablo Velasquez-Rodriguez: Titchmarsh Theorems for Hoelder- Lipschitz functions on profinite groups.- Xuechao Wang, Sven Nomm, Junqing Huang, Marianna Chatzakou, Michael Ruzhansky: An efficient neural network for the diagnosis of Parkinson’s disease using dynamic handwriting analysis.- II. Classical and non-classical problems of PDEs.- Irfan Ali: On q2-analogue of the one-dimensional non-homogeneous heat equation.- Ravshan Ashurov, Oqila Mukhiddinova: Non-local and inverse problems for the Rayleigh-Stokes equation.- Marianna Chatzakou, Abhilash Tushir: Very weak solution of the discrete Heat Equation with irregular time-dependent thermal conductivity.- Mulugeta A. Dagnaw: On a Mixed Stokes Problem with Variable Viscosity in the 2D Exterior Domain.- Nurbek Kakharman: The mixed initial-boundary value problem for degenerate hyperbolic equation.- Tynysbek Sh. Kalmenov: A criterion for minimality of the mixed type operators.- Baltabek Kanguzhin, Zhalgas Kaiyrbek: An analogue of the d’Alembert formula for the Gurtin-Pipkin equation with multipoint boundary conditions for zero initial data.- Bakytbek Koshanov, Maksat Bakytbek: On Fredholm solvability and on the index of the generalized Neumann problem for an elliptic equation of highorder on a plane.- Nedyu Popivanov, Todor Popov, Ingo Witt: Solutions with power type orexponential singularity for (3+1)-D Protter-Morawetz problems.- Makhmud Sadybekov, Batirkhan Turmetov: Boundary Value Problems for Differential Equations with a High-Order Derivative in the boundary condition.- Serikbol Shaimardan: A Cauchy problem for q-heat equation.- Marian Slodicka: Evolutionary PDEs with Volterra operators: direct and inverse source problems.- Karel Van Bockstal: Inverse source problems in thermoelasticity.- Rong Zhang: A Direct Method of Moving Planes for Logarithmic Schroedinger Operator.

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".