Umfang:
1 online resource (473 pages)
ISBN:
9789812794550
Inhalt:
Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws. Sample Chapter(s). Hyperbolic Equations, Waves and the Singularity Theory (858 KB). Contents: Boundary Value Problems and Initial Value Problems for Partial Differential Equations; Applications of Functional-Analytic and Complex Methods to Mathematical Physics; Partial Complex Differential Equations in the Plane; Complex Methods in Higher Dimensions. Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics.
Inhalt:
Intro -- CONTENTS -- Preface -- 1 Boundary value problems and initial value problems for partial differential equations -- Hyperbolic equations, waves and the singularity theory -- On the regularity of solutions of the first boundary problem for higher order hyperbolic differential equations -- Zeilon's operator and lacunae -- Representation of the Stokes potential in divergence form -- On spectra of the operator rotor -- Algebraic properties of potential differential and pseudodifferential operators -- The method of weighted function spaces for solving initial value and boundary value problems -- The optimization of fixed-point methods -- Principle of Telethoscope -- Isometric mappings and the problem of A. D. Aleksandrov for conservative distances -- Natural metrics of differential equations (abstract) -- Embedding theorems in anisotropic functional spaces (abstract) -- Distributional analysis of boundary value problems in half-spaces-exemplifled by Melan's problem of elastostatics (abstract) -- Bäcklund transformations and nonlinear evolution equations (ABSTRACT) -- Nonlinear perturbations of systems of partial differential equations (ABSTRACT) -- Partial differential equations and cubature formulas (ABSTRACT) -- 2 Applications of functional-analytic and complex methods to mathematical physics -- Conservation laws for differential equations -- Applied quatemionic analysis. Maxwell's system and Dirac's equation -- Integral transforms method in the conjugation problems of electromagnetic fields -- Remarks on fundamental matrices (Green's Tensors) in elastodynamics, piezoelectricity and crystal optics -- Dynamical problems in the (0,0) and (1,0) approximations of a mathematical model of cusped bars -- Vanishing viscosity limit of the incompressible Navier-Stokes equation (ABSTRACT) -- 3 Partial complex differential equations in the plane.
Anmerkung:
Description based on publisher supplied metadata and other sources
Weitere Ausg.:
9789810247645
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Functional-analytic and complex methods, their interaction and applications to partial diffenrential equations River Edge, NJ [u.a.] : World Scientific, 2001 9810247648
Sprache:
Englisch
Schlagwort(e):
Funktionalanalysis
;
Partielle Differentialgleichung
;
Konferenzschrift
URL:
Volltext
(lizenzpflichtig)
