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Stationary Diffraction by Wedges - Alexander Komech, Anatoli Merzon

Stationary Diffraction by Wedges

Method of Automorphic Functions on Complex Characteristics
Buch | Softcover
XI, 167 Seiten
2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-26698-1 (ISBN)
CHF 67,35 inkl. MwSt

This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach.

Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann-Hilbert problem.

The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.


- Introduction. - Part I Survey of Diffraction Theory. - The Early Theory of Diffraction. - Fresnel-Kirchhoff Diffraction Theory. - Stationary and Time-Dependent Diffraction. - The Sommerfeld Theory of Diffraction by Half-Plane. - Diffraction byWedge After Sommerfeld's Article. - Part II Method of Automorphic Functions on Complex Characteristics. - Stationary Boundary Value Problems in Convex Angles. - Extension to the Plane. - Boundary Conditions via the Cauchy Data. - Connection Equation on the Riemann Surface. - On Equivalence of the Reduction. - Undetermined Algebraic Equations on the Riemann Surface. - Automorphic Functions on the Riemann Surface. - Functional Equation with a Shift. - Lifting to the Universal Covering. - The Riemann-Hilbert Problem on the Riemann Surface. - The Factorization. - The Saltus Problem and Final Formula. - The Reconstruction of Solution and the Fredholmness. - Extension of the Method to Non-convex Angle. - Comments.

Erscheinungsdatum
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo XI, 167 p. 19 illus., 3 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 284 g
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte automorphic functions • Boundary value problem • Complex Fourier Transform • diffraction • distributions • elliptic equation • Factorization • Fredholm operators • Helmholtz equation • Holomorphic Functions • Paley-Wiener theorem • Partial differential equations • pseudo-differential operators • Riemann-Hilbert problem • Riemann surface • Wedge
ISBN-10 3-030-26698-2 / 3030266982
ISBN-13 978-3-030-26698-1 / 9783030266981
Zustand Neuware
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