New Trends in the Applications of Differential Equations in Sciences: NTADES 2022, Sozopol, Bulgaria, June 14–17 (Springer Proceedings in Mathematics & Statistics, 412)

This book convenes peer-reviewed, selected papers presented at the Ninth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Sozopol, Bulgaria, June 17–20, 2022. The works are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis. In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them for solving real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations. The NTADES 2022 conference was organized in cooperation with the Society of Industrial and Applied Mathematics (SIAM), the major international organization for Industrial and Applied Mathematics and for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering, finance, and neuroscience. Preface Contents Applications in Mathematical Physics Porous-Media Flow and Yamabe Flow on Complete Manifolds 1 Introduction to Porous-Media (PM) Equation and Yamabe Flow 1.1 Porous-Media Equation 1.2 Scalar Curvature Problems on Compact Manifolds 1.3 Scalar Curvature Problem on Complete Manifolds 1.4 Yamabe Flow 2 Zero and Negative Constant Scalar Curvature Problem and Yamabe Flow 3 Monotone Methods for Yamabe Flows and Sigma PM Flows 4 Global Yamabe Flows on Rn and on Singular Manifolds 4.1 Global Yamabe Flow on Rn 4.2 Global Yamabe Flow on Singular Manifolds References Simple Equations Method (SEsM): Areas of Possible Applications 1 Introduction 2 Simple Equations Method (SEsM) 3 Kinds of Nonlinearities Treated by SEsM 4 Concluding Remarks References An Example for Application of the Simple Equations Method for the Case of Use of a Single Simple Equation 1 Introduction 2 Methodology of the Method of Simple Equations (SEsM) 3 An Example of Use of Composite Functions in the Methodology of SEsM 4 Concluding Remarks References Boundary Value Problems for the Polyharmonic Operators 1 Introduction 2 Formulation of the Main Results, Illustrative Examples, and Comments 3 Proofs of Main Results, the Examples, and Comments References Search of Complex Transcendental Roots of a Combination of a Nonlinear Equation and a Polynomial 1 Introduction 2 Analysis 2.1 From the 7th Power Equation 2.2 Form of Quintic Equation 2.3 Form of Cubic Equation 2.4 Briot–Bouquet Differential Equation 2.5 Briot–Bouquet Differential Equation of Order 2 Type 2.6 Definite Integral of a Special Function 2.7 Definite Integral Including a Special Function 2.8 Inverse Function 2.9 Nonlinear Second-Order Ordinary Differential Equation, Resulting in Two-Point Boundary Value Problem 2.10 Nonlinear Differential Equation Exactly Expressible Through Weierstrass Function 2.11 One Internal Gas Explosion Equation 2.12 Mathematical Differential Model From Modified Chandrasekhar's White Dwarf Equation 2.13 Mathematical Coupled Differential Model From Laminar Natural Vertical Convection along a Constant Temperature Wall 2.14 Integro-Differential Problem of Volterra 3 Zero-Points of Some Gauss Hypergeometric Functions 4 Conclusions References Null Non-controllability for Singular and Degenerate Heat Equation with Double Singular Potential 1 Introduction 2 Preliminaries 3 Null Non-controllability for μ>Cl,n 4 Global Existence for μ