Differential Equations, Mathematical Modeling and Computational Algorithms: DEMMCA 2021, Belgorod, Russia, October 25–29

Description

This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics. Preface Contents Some Classes of Quasilinear Equations with Gerasimov—Caputo Derivatives 1 Introduction 2 Non-degenerate Linear Equation 3 Quasilinear Equation 4 Degenerate Quasilinear Equation 5 Examples References On the Solvability of Initial Problems for Abstract Singular Equations Containing Fractional Derivatives 1 Introduction 2 Generalized Euler–Poisson–Darboux Differential Equation 3 Generalized Functional-Differential Bessel–Struve Equation 4 Appendix References Local Bifurcations of Periodic Traveling Waves in the Generalized Weakly Dissipative Ginzburg-Landau Equation 1 Introduction 2 Formulation of the Problem 3 Stability Analysis of Periodic Traveling Waves 4 Turing—Prigogine Bifurcation 5 Conclusions References Towards Discrete Octonionic Analysis 1 Introduction 2 Preliminaries and Notations 2.1 Continuous Octonionic Analysis 2.2 Discretisation of Octonionic Analysis 3 The Discrete Stokes' Formula in Octonions 4 Summary References Axiomatic Method for Constructing a Generalized Solution of a Mixed Problem for a Telegraph Equation 1 Introduction 2 A Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Deviation 3 Mixed Problem for an Inhomogeneous Wave Equation with Zero Initial Deviation 4 A Mixed Problem for an Inhomogeneous Wave Equation with a Nonzero Initial Deviation 5 Mixed Problem for the Telegraph Equation 6 The Term-by-Term Integration Theorem References Non-local Substitutions for Liouville Equations with Three and Four Independent Variables 1 On the Group Properties of Bianchi Equations 2 Three-Dimensional Analogue of the Liouville Equation 3 Fourth-Order Analogue of the Liouville Equation References Convergence Rates of a Finite Difference Method for the Fractional Subdiffusion Equations 1 Introduction 2 Discretization Methods 2.1 Spatial Semidiscrete Schemes 2.2 Fully Discrete Schemes 2.3 Regularity of the Solutions 3 Truncation Errors 4 Global Error Analysis 5 Numerical Results 6 Conclusion References Degenerate Quasilinear Equations with Dzhrbashyan—Nersesian Derivatives and Applications 1 Introduction 2 Quasilinear Nondegenerate Equation 3 Quasilinear Degenerate Equation 4 Fractional Models of Viscoelastic Fluid Dynamics References On a K-Homogeneous Metric 1 K-Homogeneous Metric 2 Investigation of Isometric Transformations for the K-Homogeneous Kipriyanov Metric 3 Characteristics of the K-Homogeneous Kipriyanov Metric in the Case of a Single Singular Variable 4 Investigation of Geodesic Lines for a K-Homogeneous Kipriyanov Metric References Biooscillators in Models of Genetic Networks 1 Introduction 2 General Models 3 Four-Dimensional Systems 4 Three-Dimensional Systems and Six-Dimensional Systems 5 Notes and Comments References Numerical Method for Problem of Scattering by a Small Thickness Dielectric Layer on a Perfectly Conductive Substrate 1 Problem Statement 2 Reduction of the Problem to Integral Equations 3 Numerical Scheme 4 Calculation Examples and Discussion References Invariants of Dynamical Systems with Dissipation on Tangent Bundles of Low-Dimensional Manifolds 1 Introduction 2 Example: Plane Pendulum in a Jet Flow 3 Example of More General System with One Degree of Freedom 4 Invariants of Systems of Geodesic Equations 5 Invariants of Potential Systems 6 Invariants of Systems with Alternating Dissipation 7 Spatial Pendulum in the Flow of the Incoming Medium References B-subharmonic Functions 1 Introduction 2 Definitions 3 B-harmonic Functions 4 Weighted Spherical Mean 5 B-subharmonic Functions References Some Multi–dimensional Modified G- and H-Integral Transforms on mathfrakLoverlineν, overliner-Spaces 1 Introduction 2 Preliminaries 3 mathfrakLoverlineν,overliner-Theory And the Inversion Formulas for the Modified H1 σ,κ-Transform 4 mathfrakLoverlineν,overliner-Theory and the Inversion Formulas of the Modified G1σ, κ- transform 5 mathfrakLoverlineν,overliner-Theory and the Inversion Formulas of the Modified G1σ, κ;δ-Transform References On Sufficient Conditions of the Faddeev–Marchenko Theorem References Variational Approach to Construction of Piecewise-Constant Approximations of the Solution of Dynamic Reconstruction Problem 1 Introduction 2 Previously Obtained Results 2.1 Dynamics 2.2 Input Data 2.3 Assumptions 2.4 Dynamic Reconstruction Problem 2.5 Algorithm 2.6 The Main Result 3 The New Results 3.1 New DRP Statement 3.2 Algorithm for Solving the New DRP 3.3 The Main Result 4 Example 5 Conclusion References Discrete Operators and Equations: Analysis and Comparison 1 Introduction 2 The Concept of the Research 2.1 Local Discrete Operators 2.2 Discrete and Continual 2.3 Infinite and Finite 3 Discrete Functional Spaces 4 Approximate Solutions 4.1 Infinite Discrete Solutions 4.2 Finite Discrete Solutions References Pseudo-Differential Equations in Spaces of Different Smoothness Exponents on Variables 1 Introduction 2 Elliptic Pseudo-differential Operators 2.1 Sobolev–Slobodetskii Spaces of Different Smoothness 2.2 Model Operators and Equations References Thermodynamic Limit in Vector Lattice Models 1 Introduction 2 The Gibbs Random Fields 3 The Hamiltonians Space Hν of Limit Gibbs Fields 4 The Extensive Asymptotics of Free Energy 5 Conclusion References Family of Smooth Solutions of Hyperbolic Differential-Difference Equation 1 Introduction 2 Construction of Solutions of Equation (1) 3 Existence of Smooth Solutions of the Equation (1) References