Generalized Functions Method in Boundary Value Problems for Wave Equations
Series: Industrial and Applied Mathematics;
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Product details:
- Publisher Springer Nature Singapore
- Date of Publication 14 February 2026
- ISBN 9789819528011
- Binding Hardback
- No. of pages154 pages
- Size 235x155 mm
- Language English
- Illustrations XXII, 154 p. 30 illus., 10 illus. in color. 700
Categories
Long description:
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This monograph presents the method of generalized functions and the method of boundary integral equations for solving nonstationary and stationary boundary value problems for classical hyperbolic equations of mathematical physics and electrodynamics: the wave equation, the Klein–Gordon equation, the Schrödinger equation and the system of Maxwell equations in spaces of dimension 1, 2, 3. It also discusses the theory of generalized functions for solving hyperbolic equations and systems described by pseudo-differential operators. The monograph studies the processes of shock waves, which is often simply impossible within the framework of the classical theory of differential equations. Generalized solutions of the considered boundary value problems, their regular integral representations and resolving singular boundary integral equations have been constructed, which belong to a new class of boundary integral equations, which can become the subject of a separate study in the field of functional analysis and function theory.
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Basic Concepts of Generalized Functions Theory: Fundamental Solutions and their Properties.- Integral Equations of Boundary Value Problems for Schrodinger–Gordon–Fock Equation: Scattering Amplitude.- Nonstationary Boundary Value Problems for d’Alembert Wave Equation and their Solutions.- Boundary Integral Equations of Nonstationary Boundary Value Problems for the Klein–Gordon–Fock Equation.- Generalized Solutions of Transport Boundary Value Problems for Wave Equation.- Fundamental and Generalized Solutions of Maxwell Equations and their Properties.- Generalized Solutions of Stationary Boundary Value Problems for Maxwell Equations.- Generalized Solutions of Nonstationary Boundary Value Problems for Maxwell Equations.
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