The asymptotic analysis of boundary value problems in parameter-dependent domains is a rapidly developing field of research in the theory of partial differential equations, with important applications in electrostatics, elasticity, hydrodynamics and fracture mechanics. Building on the work of Ciarlet and Destuynder, this book provides a systematic coverage of these methods in multi-structures, i.e. domains which are dependent on a small parameter e in such a way that the limit region consists of subsets of different space dimensions. An undergraduate knowledge of partial differential equations and functional analysis is assumed.
The asymptotic analysis of boundary value problems in parameter-dependent domains is a rapidly developing field of research in the theory of partial differential equations, with important applications in electrostatics, elasticity, hydrodynamics and fracture mechanics. Building on the work of Ciarlet and Destuynder, this book provides a systematic coverage of these methods in multi-structures, i.e. domains which are dependent on a small parameter e in such a way that the limit region consists of subsets of different space dimensions. An undergraduate knowledge of partial differential equations and functional analysis is assumed.
1: Introduction to compound asymptotic expansions
2: A boundary value problem for the Laplacian in a
multi-structure
3: Auxiliary facts from mathematical elasticity
4: Elastic multi-structure
5: Non-degenerate elastic multi-structure
6: Spectral analysis for 3D-1D multi-structures
Bibliographical remarks
Bibliography
Index
"This book deals with mixed boundary value problems for the Laplace operator or the Lamé system in multi-structures. . . The approach is based upon the method of compound asymptotic expansions . . . The whole asymptotic procedure is rigorously justified." -- Mathematical Reviews
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