Analysis and Applied Mathematics

This book presents extended abstracts of the Analysis and Applied Mathematics seminar organized jointly by Bahçeehir University, Istanbul, Turkey, Ghent Analysis & PDE Center, Ghent University, Ghent, Belgium and the Institute Mathematics & Math. Modeling, Almaty, Kazakhstan. The book is of value to professional mathematicians as well as advanced students in the fields of analysis and applied mathematics. The goal of the seminar is to provide a forum for researchers and scientists from different regions to communicate their recent developments and to present their original results in various fields of analysis and applied mathematics. All of the articles contain new results and are peer-reviewed. The volume reflects the latest developments in the area of analysis and applied mathematics and their interdisciplinary applications.

Reflects the latest developments in analysis and applied mathematics and their interdisciplinary applications Provides visions of professional experts in the field of analysis and applied mathematics Includes real-world applications and emphasis on computational skills

Autorentext

Allaberen Ashyralyev is a professor of mathematics at Bahçe ehir University, Istanbul, Türkiye

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.

Makhmud A. Sadybekov is Director General at the Institute of Mathematics and Mathematical Modelling in Almaty, Kazakhstan.

Inhalt

• Part I Analysis.- Some Measures of Noncompactness and Their Applications.- Definition of Hessians for m--convex Functions as Borel Measures.- Necessary and Sufficient Conditions for Basis Properties of the System of Root Functions of Sturm-Liouville Boundary Value Problems with Eigenparameter Dependent Boundary Conditions.- Asymptotic Analysis of SturmLiouville Problem with Two-Point Boundary Conditions.- Characterization of the Constant Sign of a Class of Periodic and Neumann Green's Functions via Spectral Theory.- Results for Multidimensional Hardy Operator Using Domain Partitions.- Part II Theory of Applied Mathematics.- A Numerical Algorithm for the Third Order Delay Partial Differential Equation with Robin Boundary Condition.- Solution of the Problem of Generalized Localization for Spherical Partial Sums of Multiple Fourier Series.- Regularization Methods for Solving Inverse Problems: A Comprehensive Review.- The Application of Spectral Resolution of a Self-Adjoint Operator to Approximate Elliptic Source Identification Problem with Neumann-Type Integral Condition.- A Note on Numerical Solution of a Parabolic Source Identification Problem with Involution and Robin Condition.- Part III Differential Equations and Their Applications.- On Sixth Order of Accuracy Four-Step Difference Schemes for the Fourth-Order Differential Equations.- Study of the Problem of One-Dimensional Flow of Homogenous Fluids in Fractal Porous Media.- Nonlocal Initial-Boundary Value Problems for a Degenerate Hyperbolic Equation.- On Well-Posedness of the Nonlocal Boundary Value Problem with Samarskii-Ionkin Conditions for the 2m-th Order Multidimensional Elliptic Equations.- Smoothness for Degenerate Elliptic Equations with Matrix Weights.- Stability Analysis of Differential Equations Using Mohand Integral Transform.- Part IV Modeling and Applications.- Mathematical Issues of Difference Schemes for Atmospheric Boundary Layer Equations.- Application of Adjoint Equations for Numerical Solution of Problems Using the Fictitious Domain Method.- Numerical Modeling of Diffusion Processes with Variable Density and Source in Two-Componential Nonlinear Media.- An Extensive Simulation Study for Evaluation of Penalized Variable Selection.- Constrained Switching of Exponentially Stable Time-Delay Systems: Perspectives and Open Questions.- A Regularization Method for an Inverse Problem Represented by a First-Kind Integral Equation.