"Mathematical Theorems: Boundary Value Problems and Approximations" ed. by Lyudmila Alexeyeva

The main content of this book is related to construction of analytical solutions of differential equations and systems of mathematical physics, to development of analytical methods for solving boundary value problems for such equations and the study of properties of their solutions. The book is intended for specialists in the field of mathematical and theoretical physics, mechanics and biophysics, students of mechanics, mathematics, physics and biology departments of higher educational institutions.

A wide class of equations (elliptic, parabolic, and hyperbolic) is considered here, on the basis of which complex wave processes in biological and physical media can be simulated. The method of generalized functions presented in the book for solving boundary value problems of mathematical physics is universal for constructing solutions of boundary value problems for systems of linear differential equations with constant coefficients of any type. In the last sections of the book, the issues of calculating functions based on Padé approximations, binomial expansions, and fractal representations are considered.

Contents
1. Exact Traveling Wave Solutions of One-Dimensional Parabolic-Parabolic Models of Chemotaxis
2. Generalized and Fundamental Solutions of Motion Equations of Two-Component Biot’s Medium
3. Boundary Integral Equations of no Stationary Boundary Value Problems for the Klein-Gordon Equation
4. Singular Boundary Integral Equations of Boundary Value Problems for Hyperbolic Equations of Mathematical Physics
5. Padé Approximation to Solve the Problems of Aerodynamics and Heat Transfer in the Boundary Layer
6. Alternative Representation for Binomials and Multinomies and Coefficient Calculation
7. How Are Fractal Interpolation Functions Related to Several Contractions?


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