Generalized Functions Method in Boundary Value Problems for Wave Equations
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Beschreibung
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.
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.
Explores groundbreaking methods for solving boundary value problems in hyperbolic equations using generalized functions Discusses unique approaches to studying shock waves and discontinuous solutions in mathematical physics Advances the knowledge by dedicating the study entirely to hyperbolic equations and boundary value problems
Autor*in
Lyudmila Alexeyeva
Themen in »Generalized Functions Method in Boundary Value Problems for Wave Equations«
generalized functons mathematical physics electrodynamics boundary value problems integral equations Schrodinger– Gordon–Fock equation scattering amplitude d’Alembert wave equation Klein–Gordon–Fock equation Maxwell equations