Integral Methods in Science and Engineering -

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Résumé :
This self-contained work illustrates the application of integral methods to diverse problems in mathematics, physics, biology, and engineering. The thirty two chapters of the book 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. Integral Methods in Science and Engineering is a useful and practical guide to a variety of topics of interest to pure and applied mathematicians, physicists, biologists, and civil and mechanical engineers, at both the professional and graduate student level....

Sommaire:
Superconvergence of Projection Methods for Weakly Singular Integral Operators.- On Acceleration of Spectral Computations for Integral Operators with Weakly Singular Kernels.- Numerical Solution of Integral Equations in Solidification and Melting with Spherical Symmetry.- An Analytic Solution for the Steady-State Two-Dimensional Advection-Diffusion-Deposition Model by the GILTT Approach.- Analytic Two-Dimensional Atmospheric Pollutant Dispersion Simulation by Double GITT.- Transient Acoustic Radiation from a Thin Spherical Elastic Shell.- The Eigenfrequencies and Mode Shapes of Drilling Masts.- Layer Potentials in Dynamic Bending of Thermoelastic Plates.- Direct Methods in the Theory of Thermoelastic Plates.- The Dirichlet Problem for the Plane Deformation of a Thin Plate on an Elastic Foundation.- Some Remarks on Homogenization in Perforated Domains.- Dynamic Response of a Poroelastic Half-Space to Harmonic Line Tractions.- Convexity Conditions and Uniqueness and Regularity of Equilibria in Nonlinear Elasticity.- The Mathematical Modeling of Syringomyelia.- A System Iterative Method for Solving First-Kind, Degraded Identity Operator Equations.- Fast Numerical Integration Method Using Taylor Series.- Boundary Integral Solution of the Two-Dimensional Fractional Diffusion Equation.- About Traces, Extensions, and Co-Normal Derivative Operators on Lipschitz Domains.- On the Extension of Divergence-Free Vector Fields Across Lipschitz Interfaces.- Solutions of the Atmospheric Advection-Diffusion Equation by the Laplace Transformation.- On Quasimodes for Spectral Problems Arising in Vibrating Systems with Concentrated Masses.- Two-Sided Estimates for Local Minimizers in Compressible Elasticity.- Harmonic Oscillations in a Linear Theory of Antiplane Elasticity with Microstructure.- Exterior Dirichlet and Neumann Problems for the Helmholtz Equation as Limits of Transmission Problems.- Direct Boundary Element Method with Discretization of All Integral Operators.- Reciprocity in Elastomechanics: Development of Explicit Results for Mixed Boundary Value Problems.- Integral Equation Modeling of Electrostatic Interactions in Atomic Force Microscopy.- Integral Representation for the Solution of a Crack Problem Under Stretching Pressure in Plane Asymmetric Elasticity.- Euler-Bernoulli Beam with Energy Dissipation: Spectral Properties and Control.- Correct Equilibrium Shape Equation of Axisymmetric Vesicles.- Properties of Positive Solutions of the Falkner-Skan Equation Arising in Boundary Layer Theory.- Stabilization of a Four-Dimensional System under Real Noise Excitation.