Ebook: Integral Methods in Science and Engineering, Volume 1: Analytic Methods
- Tags: Integral Equations, Appl.Mathematics/Computational Methods of Engineering, Ordinary Differential Equations, Partial Differential Equations, Mechanical Engineering, Mathematical Methods in Physics
- Year: 2010
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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
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
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
Content:
Front Matter....Pages 1-14
Homogenization of the Integro-Differential Burgers Equation....Pages 1-8
Geometric Versus Spectral Convergence for the Neumann Laplacian under Exterior Perturbations of the Domain....Pages 9-19
Dyadic Elastic Scattering by Point Sources: Direct and Inverse Problems....Pages 21-28
Two-Operator Boundary–Domain Integral Equations for a Variable-Coefficient BVP....Pages 29-39
Solution of a Class of Nonlinear Matrix Differential Equations with Application to General Relativity....Pages 41-51
The Bottom of the Spectrum in a Double-Contrast Periodic Model....Pages 53-63
Fredholm Characterization of Wiener–Hopf–Hankel Integral Operators with Piecewise Almost Periodic Symbols....Pages 65-74
Fractal Relaxed Problems in Elasticity....Pages 75-84
Hyers–Ulam and Hyers–Ulam–Rassias Stability of Volterra Integral Equations with Delay....Pages 85-94
Fredholm Index Formula for a Class of Matrix Wiener–Hopf Plus and Minus Hankel Operators with Symmetry....Pages 95-104
Invertibility of Singular Integral Operators with Flip Through Explicit Operator Relations....Pages 105-114
Contact Problems in Bending of Thermoelastic Plates....Pages 115-122
On Burnett Coefficients in Periodic Media with Two Phases....Pages 123-133
On Regular and Singular Perturbations of the Eigenelements of the Laplacian....Pages 135-148
High-Frequency Vibrations of Systems with Concentrated Masses Along Planes....Pages 149-159
On J. Ball’s Fundamental Existence Theory and Regularity of Weak Equilibria in Nonlinear Radial Hyperelasticity....Pages 161-171
The Conformal Mapping Method for the Helmholtz Equation....Pages 173-177
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....Pages 179-182
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....Pages 183-192
On Different Quasimodes for the Homogenization of Steklov-Type Eigenvalue Problems....Pages 193-204
Asymptotic Analysis of Spectral Problems in Thick Multi-Level Junctions....Pages 205-215
Integral Approach to Sensitive Singular Perturbations....Pages 217-234
Regularity of the Green Potential for the Laplacian with Robin Boundary Condition....Pages 235-243
On the Dirichlet and Regularity Problems for the Bi-Laplacian in Lipschitz Domains....Pages 245-254
Propagation of Waves in Networks of Thin Fibers....Pages 255-278
Homogenization of a Convection–Diffusion Equation in a Thin Rod Structure....Pages 279-290
Existence of Extremal Solutions of Singular Functional Cauchy and Cauchy–Nicoletti Problems....Pages 291-300
Asymptotic Behavior of the Solution of an Elliptic Pseudo-Differential Equation Near a Cone....Pages 301-305
Averaging Normal Forms for Partial Differential Equations with Applications to Perturbed Wave Equations....Pages 307-321
Internal Boundary Variations and Discontinuous Transversality Conditions in Mechanics....Pages 323-332
Regularization of Divergent Integrals in Boundary Integral Equations for Elastostatics....Pages 333-345
Back Matter....Pages 1-3
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
Content:
Front Matter....Pages 1-14
Homogenization of the Integro-Differential Burgers Equation....Pages 1-8
Geometric Versus Spectral Convergence for the Neumann Laplacian under Exterior Perturbations of the Domain....Pages 9-19
Dyadic Elastic Scattering by Point Sources: Direct and Inverse Problems....Pages 21-28
Two-Operator Boundary–Domain Integral Equations for a Variable-Coefficient BVP....Pages 29-39
Solution of a Class of Nonlinear Matrix Differential Equations with Application to General Relativity....Pages 41-51
The Bottom of the Spectrum in a Double-Contrast Periodic Model....Pages 53-63
Fredholm Characterization of Wiener–Hopf–Hankel Integral Operators with Piecewise Almost Periodic Symbols....Pages 65-74
Fractal Relaxed Problems in Elasticity....Pages 75-84
Hyers–Ulam and Hyers–Ulam–Rassias Stability of Volterra Integral Equations with Delay....Pages 85-94
Fredholm Index Formula for a Class of Matrix Wiener–Hopf Plus and Minus Hankel Operators with Symmetry....Pages 95-104
Invertibility of Singular Integral Operators with Flip Through Explicit Operator Relations....Pages 105-114
Contact Problems in Bending of Thermoelastic Plates....Pages 115-122
On Burnett Coefficients in Periodic Media with Two Phases....Pages 123-133
On Regular and Singular Perturbations of the Eigenelements of the Laplacian....Pages 135-148
High-Frequency Vibrations of Systems with Concentrated Masses Along Planes....Pages 149-159
On J. Ball’s Fundamental Existence Theory and Regularity of Weak Equilibria in Nonlinear Radial Hyperelasticity....Pages 161-171
The Conformal Mapping Method for the Helmholtz Equation....Pages 173-177
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....Pages 179-182
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....Pages 183-192
On Different Quasimodes for the Homogenization of Steklov-Type Eigenvalue Problems....Pages 193-204
Asymptotic Analysis of Spectral Problems in Thick Multi-Level Junctions....Pages 205-215
Integral Approach to Sensitive Singular Perturbations....Pages 217-234
Regularity of the Green Potential for the Laplacian with Robin Boundary Condition....Pages 235-243
On the Dirichlet and Regularity Problems for the Bi-Laplacian in Lipschitz Domains....Pages 245-254
Propagation of Waves in Networks of Thin Fibers....Pages 255-278
Homogenization of a Convection–Diffusion Equation in a Thin Rod Structure....Pages 279-290
Existence of Extremal Solutions of Singular Functional Cauchy and Cauchy–Nicoletti Problems....Pages 291-300
Asymptotic Behavior of the Solution of an Elliptic Pseudo-Differential Equation Near a Cone....Pages 301-305
Averaging Normal Forms for Partial Differential Equations with Applications to Perturbed Wave Equations....Pages 307-321
Internal Boundary Variations and Discontinuous Transversality Conditions in Mechanics....Pages 323-332
Regularization of Divergent Integrals in Boundary Integral Equations for Elastostatics....Pages 333-345
Back Matter....Pages 1-3
....