Description
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. This illustrative model was chosen because of its practical importance and some unusual mathematical features, but the solution technique can easily be adapted to many other hyperbolic systems of partial differential equations arising in continuum mechanics. Igor Chudinovich is Professor of Mathematics at the University of Guanajuato, Mexico, and Christian Constanda is Oliphant Professor of Mathematical Sciences at the University of Tulsa, USA. 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.- Plate on a Generalized Elastic Foundation.- Problems with Nonhomogeneous Equations and Nonhomogeneous Initial Conditions.- Appendix A: The Fourier and Laplace Transforms of Distributions.- References.- Index.
