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Variational and potential methods for a class of linear hyperbolic [pdf]

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes by Igor Chudinovich, Christian Constanda

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About this book :-
Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes written by Igor Chudinovich, Christian Constanda.
The problems discussed in this book include those with Dirichlet and Neumann boundary conditions (corresponding, in particular, to the clamped-edge and free-edge plate), with elastic (Robin), mixed, and combined displacementtraction (simply supported edge) boundary data, transmission (contact) problems, problems for plates with homogeneous inclusions, plates with cracks, and plates on a generalized elastic foundation. For each of them, the variational version is formulated and its solvability is examined in spaces of distributions; subsequently, the solutions are found in the form of time-dependent single-layer and double-layer potentials with distributional densities that satisfy nonstationary integral equations. The analysis technique consists in using the Laplace transformation to reduce the original problems to boundary value problems depending on the transformation parameter, and on establishing estimates for the solutions of the latter that allow conclusions to be drawn about the existence and properties of the solutions to the given initialboundary value problems. The transformed problems are solved by means of specially constructed algebras of singular integral operators defined by the boundary values of the transformed potentials.

Book Detail :-
Title: Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes
Edition:
Author(s): Igor Chudinovich, Christian Constanda
Publisher: Springer-Verlag London
Series: Springer Monographs in Mathematics
Year: 2005
Pages: 152
Type: PDF
Language: English
ISBN: 978-1-85233-888-6,978-1-84628-120-4
Country: US
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About Author :-

About Author :-
The author Christian Constanda , MS, PhD, DSc, The Charles W. Oliphant Professor of Mathematical Sciences, The University of Tulsa, 600 South College Avenue, Tulsa, Oklahoma 74104, USA.
The author Igor Chudinovich , MS, PhD, DSc, Christian Constanda MS, PhD, DSc (auth.).

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Book Contents :-
Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes written by Igor Chudinovich, Christian Constanda cover the following topics.
Preface
1. Formulation of the Problems and Their Nonstationary Boundary Integral Equations
2. Problems with Dirichlet Boundary Conditions
3. Problems with Neumann Boundary Conditions
4. Boundary Integral Equations for Problems with Dirichlet and Neumann Boundary Conditions
5. Transmission Problems and Multiply Connected Plates
6. Plate Weakened by a Crack
7. Initial-Boundary Value Problems with Other Types of Boundary Conditions
8. Boundary Integral Equations for Plates on a Generalized Elastic Foundation
9. Problems with Nonhomogeneous Equations and Nonhomogeneous Initial Conditions
A The Fourier and Laplace Transforms of Distributions
References
Index


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