Integral methods in science and engineering v. 1 Analytic methods

Mathematical models, based on ordinary, partial differential, integral, and integro-differential equations, are the only viable tool for studying our physical surroundings and their natural manifestations. Therefore, it is important for practitioners to strive to find solutions to these models, either analyticor numerical. This two-volume set gathers up-to-date research results that show how to set up a very important class of such tools, and how to use them in specific problems of science and engineering. The two volumes contain 65 chapters, which are an outgrowth of talks presented by experienced researchers from24 countries on 5 continents at the Tenth International Conference on Integral Methods in Science and Engineering held in Santander, Spain, July 7–10, 2008. The chapters address a wide range of topics, from the construction of boundary integral methods to the application of integration-based analytic and numerical techniques to mathematical models arising in almost all aspects of today’s technological world – in particular, integral equations, finite and boundaryelements, conservation laws, and hybrid approaches. 'Integral Methods in Science and Engineering, Volume 1' is a useful research guide for pure and appliedmathematicians, physicists, biologists, and mechanical, civil, and electricalengineers, graduate students in these disciplines, and various other professionals who use integration as a fundamental technique in their research. Illustrates the application of integral methods to diverse problems in mathematics, physics, biology, and engineering Chapters written by scientists with established credentials in their fields Applications to a wide spectrum of subjects, ranging from deformable structures, to traffic flow, acoustic wave propagation,spectral computation, among others For a broad audience of graduate students,researchers, and professionals in pure and applied mathematics, physics, biology, and civil and mechanical engineering INDICE: Preface.- List of Contributors.- 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-Domain Integral Equations for a Variable-Coefficient BVP.- Solutions 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 Weiner–Hopf–Hankel Integral Operators with Piecewise Almost Periodic Symbols.- Fractal Relaxed Problems in Elasticity.- Hyers–Ulam and Hyers–Ulam–Rassias Stability of Volterra Integral Equations with Delay.- Fredholm Index Formula for a Class of Matrix Weiner–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.- OnRegular and Singular Perturbations of the Eigenelements of the Laplacian.- High-Frequency Vibrations of Systems with Concentrated Masses Along Planes.- On J. Ball’s Fundamental Existence Theory and Weak Equilibria in Nonlinear RadialHyperelasticity.- 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-Diffusion Equation in a Thin Rod Structure.- Existence of Extremal Solutions of Singular Functional Cauchy and Cauchy–Nicoletti Problems.- Asymptotic Behavior of the Solution of an Elliptic Pseudo-Differential Equation Near aCone.- 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.

• ISBN: 978-0-8176-4898-5
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 352
• Fecha Publicación: 01/11/2009
• Nº Volúmenes: 1
• Idioma: Inglés