Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes [electronic resource] /
Chudinovich, Igor.author.
Constanda, C.(Christian)
The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potential representations, and the solution of the latter in Sobolev spaces. The analysis, performed in spaces of distributions, is applicable to a wide variety of data with less smoothness than that required in the corresponding classical problems, and is very useful for constructing error estimates in numerical computations. The presentation is detailed and clear, yet reasonably concise. This illustrative model was chosen because of its practical importance and some unusual mathematical features, but the solution technique developed in the book can easily be adapted to many other hyperbolic systems of partial differential equations arising in continuum mechanics.
Description based upon print version of record.
Includes bibliographical references and index.
Formulation of the Problems and Their Nonstationary Boundary Integral Equations -- Problems with Dirichlet Boundary Conditions -- Problems with Neumann Boundary Conditions -- Boundary Integral Equations for Problems with Dirichlet and Neumann Boundary Conditions -- Transmission Problems and Multiply Connected Plates -- Plate Weakened by a Crack -- Initial-Boundary Value Problems with Other Types of Boundary Conditions -- Boundary Integral Equations for Plates on a Generalized Elastic Foundation -- Problems with Nonhomogeneous Equations and Nonhomogeneous Initial Conditions.
The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potential representations, and the solution of the latter in Sobolev spaces. The analysis, performed in spaces of distributions, is applicable to a wide variety of data with less smoothness than that required in the corresponding classical problems, and is very useful for constructing error estimates in numerical computations. The presentation is detailed and clear, yet reasonably concise. This illustrative model was chosen because of its practical importance and some unusual mathematical features, but the solution technique developed in the book can easily be adapted to many other hyperbolic systems of partial differential equations arising in continuum mechanics.
Mathematical analysis.
Calculus.
Integral equations.
Functional analysis.
Mechanics.
Mechanics, Applied.
Analysis.
Integral Equations.
Functional Analysis.
Solid Mechanics.


Springer Monographs in Mathematics