Potapenko Integral Methods in Science and Engineering

Techniques and Applications
1. Auflage 2007
ISBN: 978-0-8176-4671-4
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 298 Seiten

This self-contained work illustrates the application of integral methods to diverse problems in mathematics, physics, biology, and engineering. The chapters contain state-of-the-art information on current research in a variety of important practical disciplines. The problems examined arise in real-life processes and phenomena and use a wide range of solution techniques. This is a useful and practical guide.

Autoren/Hrsg.

Potapenko, S.

Inhaltsverzeichnis

1;Contents;5
2;Preface;8
3;List of Contributors;10
4;1 Superconvergence of Projection Methods for Weakly Singular Integral Operators;15
5;2 On Acceleration of Spectral Computations for Integral Operators with Weakly Singular Kernels;22
6;3 Numerical Solution of Integral Equations in Solidi.cation and Melting with Spherical Symmetry;30
7;4 An Analytic Solution for the Steady-State Two-Dimensional Advection–Di.usion–Deposition Model by the GILTT Approach;39
8;5 Analytic Two-Dimensional Atmospheric Pollutant Dispersion Simulation by Double GITT;48
9;6 Transient Acoustic Radiation from a Thin Spherical Elastic Shell;58
10;7 The Eigenfrequencies and Mode Shapes of Drilling Masts;66
11;8 Layer Potentials in Dynamic Bending of Thermoelastic Plates;73
12;9 Direct Methods in the Theory of Thermoelastic Plates;84
13;10 The Dirichlet Problem for the Plane Deformation of a Thin Plate on an Elastic Foundation;91
14;11 Some Remarks on Homogenization in Perforated Domains;97
15;12 Dynamic Response of a Poroelastic Half-Space to Harmonic Line Tractions;106
16;13 Convexity Conditions and Uniqueness and Regularity of Equilibria in Nonlinear Elasticity;116
17;14 The Mathematical Modeling of Syringomyelia;126
18;15 A System Iterative Method for Solving First-Kind, Degraded Identity Operator Equations;133
19;16 Fast Numerical Integration Method Using Taylor Series;141
20;17 Boundary Integral Solution of the Two-Dimensional Fractional Di.usion Equation;147
21;18 About Traces, Extensions, and Co-Normal Derivative Operators on Lipschitz Domains;155
22;19 On the Extension of Divergence-Free Vector Fields Across Lipschitz Interfaces;167
23;20 Solutions of the Atmospheric Advection–Di.usion Equation by the Laplace Transformation;177
24;21 On Quasimodes for Spectral Problems Arising in Vibrating Systems with Concentrated Masses;187
25;22 Two-Sided Estimates for Local Minimizers in Compressible Elasticity;197
26;23 Harmonic Oscillations in a Linear Theory of Antiplane Elasticity with Microstructure;207
27;24 Exterior Dirichlet and Neumann Problems for the Helmholtz Equation as Limits of Transmission Problems;213
28;25 Direct Boundary Element Method with Discretization of All Integral Operators;223
29;26 Reciprocity in Elastomechanics: Development of Explicit Results for Mixed Boundary Value Problems;233
30;27 Integral Equation Modeling of Electrostatic Interactions in Atomic Force Microscopy;243
31;28 Integral Representation for the Solution of a Crack Problem Under Stretching Pressure in Plane Asymmetric Elasticity;253
32;29 Euler–Bernoulli Beam with Energy Dissipation: Spectral Properties and Control;263
33;30 Correct Equilibrium Shape Equation of Axisymmetric Vesicles;272
34;31 Properties of Positive Solutions of the Falkner–Skan Equation Arising in Boundary Layer Theory;282
35;32 Stabilization of a Four-Dimensional System under Real Noise Excitation;289
36;Index;298