A.G. Vitushkin's Books

Introduction to Complex Analysis

By: E.M. Chirka,A.G. Vitushkin,P. Dolbeault,G.M. Khenkin

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Introduction to Complex Analysis

By: E.M. Chirka,A.G. Vitushkin,P. Dolbeault,G.M. Khenkin

From the reviews: "... In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. Some of the individual articles are reminiscent in style of the early volumes of the first Ergebnisse series and will probably prove to be equally useful as a reference; ...for the appropriate reader, they will be valuable sources of information about modern complex analysis." Bulletin of the Am.Math.Society, 1991 "... This remarkable book has a helpfully informal style, abundant motivation, outlined proofs followed by precise references, and an extensive bibliography; it will be an invaluable reference and a companion to modern courses on several complex variables." ZAMP, Zeitschrift für Angewandte Mathematik und Physik, 1990

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Page Count

252

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642615252

ISBN 13

9783642615252

Mathematical Aspects of Numerical Solution of Hyperbolic Systems

By: A.G. Kulikovskii,N.V. Pogorelov,A. Yu. Semenov

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Mathematical Aspects of Numerical Solution of Hyperbolic Systems

By: A.G. Kulikovskii,N.V. Pogorelov,A. Yu. Semenov

This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena. The authors also address a number of original "nonclassical" problems, such as shock wave propagation in rods and composite materials, ionization fronts in plasma, and electromagnetic shock waves in magnets. They show that if a small-scale, higher-order mathematical model results in oscillations of the discontinuity structure, the variety of admissible discontinuities can exhibit disperse behavior, including some with additional boundary conditions that do not follow from the hyperbolic conservation laws. Nonclassical problems are accompanied by a multiple nonuniqueness of solutions. The authors formulate several selection rules, which in some cases easily allow a correct, physically realizable choice. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes Mathematical Aspects of Numerical Solution of Hyperbolic Systems particularly valuable not only to those interested the development of numerical methods, but to physicists and engineers who strive to solve increasingly complicated nonlinear equations.

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Page Count

564

Publisher

CRC Press

Published Date

ISBN 10

0849306086

ISBN 13

9780849306082

Several Complex Variables II

Function Theory in Classical Domains Complex Potential Theory

By: G.M. Khenkin,A.G. Vitushkin

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Several Complex Variables II

Function Theory in Classical Domains Complex Potential Theory

By: G.M. Khenkin,A.G. Vitushkin

Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given.

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Page Count

267

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Springer Science & Business Media

Published Date

ISBN 10

3642578829

ISBN 13

9783642578823

Book's by A.G. Vitushkin

Introduction to Complex Analysis

Introduction to Complex Analysis

Mathematical Aspects of Numerical Solution of Hyperbolic Systems

Mathematical Aspects of Numerical Solution of Hyperbolic Systems

Several Complex Variables II

Several Complex Variables II

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