: S. Potapenko
: Integral Methods in Science and Engineering Techniques and Applications
: Birkhäuser Basel
: 9780817646714
: 1
: CHF 50.10
:
: Analysis
: English
: 298
: Wasserzeichen/DRM
: PC/MAC/eReader/Tablet
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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.
Contents5
Preface8
List of Contributors10
1 Superconvergence of Projection Methods for Weakly Singular Integral Operators15
2 On Acceleration of Spectral Computations for Integral Operators with Weakly Singular Kernels22
3 Numerical Solution of Integral Equations in Solidi.cation and Melting with Spherical Symmetry30
4 An Analytic Solution for the Steady-State Two-Dimensional Advection Di.usion Deposition Model by the GILTT Approach39
5 Analytic Two-Dimensional Atmospheric Pollutant Dispersion Simulation by Double GITT48
6 Transient Acoustic Radiation from a Thin Spherical Elastic Shell58
7 The Eigenfrequencies and Mode Shapes of Drilling Masts66
8 Layer Potentials in Dynamic Bending of Thermoelastic Plates73
9 Direct Methods in the Theory of Thermoelastic Plates84
10 The Dirichlet Problem for the Plane Deformation of a Thin Plate on an Elastic Foundation91
11 Some Remarks on Homogenization in Perforated Domains97
12 Dynamic Response of a Poroelastic Half-Space to Harmonic Line Tractions106
13 Convexity Conditions and Uniqueness and Regularity of Equilibria in Nonlinear Elasticity116
14 The Mathematical Modeling of Syringomyelia126
15 A System Iterative Method for Solving First-Kind, Degraded Identity Operator Equations133
16 Fast Numerical Integration Method Using Taylor Series141
17 Boundary Integral Solution of the Two-Dimensional Fractional Di.usion Equation147
18 About Traces, Extensions, and Co-Normal Derivative Operators on Lipschitz Domains155
19 On the Extension of Divergence-Free Vector Fields Across Lipschitz Interfaces167
20 Solutions of the Atmospheric Advection Di.usion Equation by the Laplace Transformation177
21 On Quasimodes for Spectral Problems Arising in Vibrating Systems with Concentrated Masses187
22 Two-Sided Estimates for Local Minimizers in Compressible Elasticity197
23 Harmonic Oscillations in a Linear Theory of Antiplane Elasticity with Microstructure207
24 Exterior Dirichlet and Neumann Problems for the Helmholtz Equation as Limits of Transmission Problems213
25 Direct Boundary Element Method with Discretization of All Integral Operators223
26 Reciprocity in Elastomechanics: Development of Explicit Results for Mixed Boundary Value Problems233
27 Integral Equation Modeling of Electrostatic Interactions in Atomic Force Microscopy243
28 Integral Representation for the Solution of a Crack Problem Under Stretching Pressure in Plane Asymmetric Elasticity253
29 Euler Bernoulli Beam with Energy Dissipation: Spectral Properties and Control263
30 Correct Equilibrium Shape Equation of Axisymmetric Vesicles272
31 Properties of Positive Solutions of the Falkner Skan Equation Arising in Boundary Layer Theory282
32 Stabilization of a Four-Dimensional System under Real Noise Excitation289
Index298