Generalized Analytic Functions : Theory and Applications to Mechanics

Theory and Applications to Mechanics

By: Helmut Florian (Editor), Klaus Hackl (Editor), Franz Josef Schnitzer (Editor)

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Hardcover | 1 December 2009

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340 Pages

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23.39 x 15.6 x 2.06

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An intensive development of the theory of generalized analytic functions started when methods of Complex Analysis were combined with methods of Functional Analysis, especially with the concept of distributional solutions to partial differential equations. The power of these interactions is far from being exhausted. In order to promote the further development of the theory of generalized analytic functions and applications of partial differential equations to Mechanics, the Technical University of Graz organized a conference whose Proceedings are contained in the present volume.
The contributions on generalized analytic functions (Part One) deal not only with problems in the complex plane (boundary value and initial value problems), but also related problems in higher dimensions are investigated where both several complex variables and the technique of Clifford Analysis are used. Part Two of the Proceedings is devoted to applications to Mechanics. It contains contributions to a variety of general methods such as L p-methods, boundary elements and asymptotic methods, and hemivariational inequalities. A substantial number of the papers of Part Two, however, deals with problems in Ocean Acoustics.
The papers of both parts of the Proceedings can be recommended to mathematicians, physicists, and engineers working in the fields mentioned above, as well as for further reading within graduate studies.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Complex Analysis Differential Calculus & Equations Science Physics

Preface	p. ix
Contributing Authors	p. xi
Laudatio	p. xvii
Present Trends in the Theory of Generalized Analytic Functions and Generalizations of Complex Analysis
Generalized Analytic Functions in Mathematical Analysis	p. 3
On Singular Integral Equations Approach to Generalized Analytic Functions	p. 17
On Some Classes of Pseudo-Analytic Functions	p. 27
Some Yugoslavian Contributions to the Theory of Generalized Analytic Functions	p. 33
Applications of Reproducing Kernels to Partial Differential Systems	p. 41
Transmutations in Differential Rings	p. 55
Solution of Initial Value Problems for Pseudoholomorphic Functions in Conical Domains	p. 65
The Contraction-Mapping Principle - Some Associated Optimization Problems	p. 69
On the Optimization of the Set of Definition of Operators in Applications of the Contraction-Mapping Principle to Differential Equations	p. 73
Generalized Analytic Functions in Multidimensional Spaces	p. 77
Overdetermined Systems of Second Order Elliptic Equations in Several Complex Variables	p. 89
On the Boundary Behaviour of Polyanalytic Functions of Two Variables in Jordan Bicylinders	p. 111
Generalized Analytic Functions in Differential Geometry	p. 127
The Brothers Riesz Theorem: Complex and Real Versions	p. 139
On the Theory of Series of Exponentials	p. 151
Applications of Partial Differential Equations to Mechanics	p. 155
A Boundary-Finite Element Method for Potential Flow Past an Airfoil	p. 157
Boundary Value Problems of Nonlinear Elastostatics	p. 183
On Some Regularity Results for Hemivariational Inequalities	p. 197
Underwater Acoustics	p. 215
Asymptotic Methods in Underwater Acoustics	p. 229
Comparison of the Parabolic Approximation with Residue Calculus in Ocean Acoustics	p. 241
Some Inverse Problems in Stratified Media	p. 255
A Note on the Global Existence and Decay of Solutions of Systems of Parabolic Conservation Laws	p. 265
Analytical and Numerical Treatment of Hele-Shaw Models With and Without Regularization	p. 271
Generalized Analytic Functions in Mechanics	p. 289
Integrability and the Schrodinger Equation	p. 299
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Generalized Analytic Functions : Theory and Applications to Mechanics

Theory and Applications to Mechanics

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Hardcover

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