Integral Methods in Science and Engineering, Volume 1 Analytic Methods - Perez, Maria Eugenia; SpringerLink (Online service) (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2010)
Mathematical models—including those based on ordinary, partial differential, integral, and integro-differential equations—are indispensable tools for studying the physical world and its natural manifestations. Because of the usefulness of these models, it is critical for practitioners to be able to find their solutions by analytic and/or computational means. This two-volume set is a collection of up-to-date research results that illustrate how a very important class of mathematical tools can be manipulated and applied to the study of real-life phenomena and processes occurring in specific problems of science and engineering. The two volumes contain 65 chapters, which are based on talks presented by reputable researchers in the field at the Tenth International Conference on Integral Methods in Science and Engineering. The chapters address a wide variety of methodologies, from the construction of boundary integral methods to the application of integration-based analytic and computational techniques in almost all aspects of today's technological world. Among the topics covered are deformable structures, traffic flow, acoustic wave propagation, spectral procedures, eutrophication of bodies of water, pollutant dispersion, spinal cord movement, submarine avalanches, and many others with an interdisciplinary flavor. Integral Methods in Science and Engineering, Volumes 1 and 2 are useful references for a broad audience of professionals, including pure and applied mathematicians, physicists, biologists, and mechanical, civil, and electrical engineers, as well as graduate students, who use integration as a fundamental technique in their research. Volume 1: ISBN 978-0-8176-4898-5 Volume 2: ISBN 978-0-8176-4896-1.
Homogenization of the Integro-Differential Burgers Equation -- Geometric Versus Spectral Convergence for the Neumann Laplacian under Exterior Perturbations of the Domain -- Dyadic Elastic Scattering by Point Sources: Direct and Inverse Problems -- Two-Operator Boundary#x2013;Domain Integral Equations for a Variable-Coefficient BVP -- Solution of a Class of Nonlinear Matrix Differential Equations with Application to General Relativity -- The Bottom of the Spectrum in a Double-Contrast Periodic Model -- Fredholm Characterization of Wiener#x2013;Hopf#x2013;Hankel Integral Operators with Piecewise Almost Periodic Symbols -- Fractal Relaxed Problems in Elasticity -- Hyers#x2013;Ulam and Hyers#x2013;Ulam#x2013;Rassias Stability of Volterra Integral Equations with Delay -- Fredholm Index Formula for a Class of Matrix Wiener#x2013;Hopf Plus and Minus Hankel Operators with Symmetry -- Invertibility of Singular Integral Operators with Flip Through Explicit Operator Relations -- Contact Problems in Bending of Thermoelastic Plates -- On Burnett Coefficients in Periodic Media with Two Phases -- On Regular and Singular Perturbations of the Eigenelements of the Laplacian -- High-Frequency Vibrations of Systems with Concentrated Masses Along Planes -- On J. Ball#x2019;s Fundamental Existence Theory and Regularity of Weak Equilibria in Nonlinear Radial Hyperelasticity -- The Conformal Mapping Method for the Helmholtz Equation -- Integral Equation Method in a Problem on Acoustic Scattering by a Thin Cylindrical Screen with Dirichlet and Impedance Boundary Conditions on Opposite Sides of the Screen -- Existence of a Classical Solution and Nonexistence of a Weak Solution to the Dirichlet Problem for the Laplace Equation in a Plane Domain with Cracks -- On Different Quasimodes for the Homogenization of Steklov-Type Eigenvalue Problems -- Asymptotic Analysis of Spectral Problems in Thick Multi-Level Junctions -- Integral Approach to Sensitive Singular Perturbations -- Regularity of the Green Potential for the Laplacian with Robin Boundary Condition -- On the Dirichlet and Regularity Problems for the Bi-Laplacian in Lipschitz Domains -- Propagation of Waves in Networks of Thin Fibers -- Homogenization of a Convection#x2013;Diffusion Equation in a Thin Rod Structure -- Existence of Extremal Solutions of Singular Functional Cauchy and Cauchy#x2013;Nicoletti Problems -- Asymptotic Behavior of the Solution of an Elliptic Pseudo-Differential Equation Near a Cone -- Averaging Normal Forms for Partial Differential Equations with Applications to Perturbed Wave Equations -- Internal Boundary Variations and Discontinuous Transversality Conditions in Mechanics -- Regularization of Divergent Integrals in Boundary Integral Equations for Elastostatics.
Keywords: Integral equations; Applied mathematics; Engineering mathematics; Differential equations; Partial differential equations; Mechanical engineering; Physics; Integral Equations; Mathematical and Computational Engineering; Ordinary Differential Equations; Partial Differential Equations; Mechanical Engineering; Mathematical Methods in Physics