Asymptotic theory of dynamic boundary value problems in irregular domains /
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Author / Creator: | Korikov, Dmitrii. |
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Imprint: | Cham : Birkhäuser, 2021. |
Description: | 1 online resource (404 p.). |
Language: | English |
Series: | Operator Theory, Advances and Applications ; v. 284 Operator theory, advances and applications ; v. 284. |
Subject: | |
Format: | E-Resource Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/12611909 |
Table of Contents:
- Intro
- Preface
- Contents
- 1 Introduction
- 2 Wave Equation in Domains with Edges
- 2.1 Dirichlet Problem for the Wave Equation
- 2.1.1 Function Spaces in a Wedge and in a Cone
- 2.1.2 Problem in a Wedge: Problem with Parameter in a Cone: Existence of Solutions
- 2.1.3 Weighted Combined Estimates
- 2.1.4 Operators in the Scale of Weighted Spaces
- 2.1.5 Asymptotics of Solutions Near the Vertex of a Cone or Near the Edge of a Wedge
- 2.1.6 Explicit Formulas for the Coefficients in Asymptotics
- 2.1.7 Problem in a Bounded Domain with Conical Points
- 2.1.8 Problem in a Bounded Domain: Asymptotics of Solutions Near an Internal Point
- 2.2 Neumann Problem for the Wave Equation
- 2.2.1 Statement of the Problem: Preliminaries
- 2.2.2 Weighted Combined Estimates for Solutions to Problem (2.138), (2.139)
- 2.2.3 Operator of the Boundary Value Problem in a Cone
- 2.2.4 Boundary Value Problem in a Cone in the Scale of Weighted Spaces
- 2.2.5 Asymptotic Expansions of Solutions to the Problem in a Cone
- 2.2.6 Problem in a Wedge
- 2.2.7 Explicit Formulas for the Coefficients in Asymptotics
- 2.2.8 Problem in a Bounded Domain with Conical Points
- 3 Hyperbolic Systems in Domains with Conical Points
- 3.1 Cauchy-Dirichlet Problem
- 3.1.1 Combined Estimate for Solutions of the Problem in a Cone
- 3.1.2 Operator of the Boundary Value Problem in a Cone: The Existence and Uniqueness of Solutions
- 3.1.3 The Boundary Value Problem in a Cone in the Scale of Weighted Spaces
- 3.1.4 Asymptotics of Solutions of the Problem in a Cone
- 3.1.5 The Problem in a Wedge
- 3.2 Neumann Problem
- 3.2.1 The Model Problems in a Cone: A Strong Solution
- 3.2.2 Weighted Estimates of Solutions of the Problem with Parameter in a Cone
- 3.2.3 The Problem with Parameter in a Cone: A Scale of Weighted Spaces
- 3.2.4 The Asymptotics of Solutions
- 3.2.5 A Bounded Domain with a Conical Point
- 4 Elastodynamics in Domains with Edges
- 4.1 Introduction
- 4.2 Homogeneous Energy Estimates on Solutions of Boundary Value Problems with Parameter in a Wedge
- 4.3 Nonhomogeneous Energy Estimates for Solutions of Boundary Value Problems with Parameter in a Wedge
- 4.3.1 Estimates on Solutions with Dirichlet BoundaryCondition
- 4.3.2 Estimates on Solutions with Neumann Boundary Condition
- 4.4 Strong Solutions
- 4.4.1 The Dirichlet Problem with Homogeneous Energy Estimate in a Wedge
- 4.4.2 The Dirichlet Problem with Nonhomogeneous Energy Estimate in a Wedge
- 4.4.3 The Neumann Problem in a Wedge
- 4.5 Weighted a priori Estimates for Solutions of Boundary Value Problems with Parameter in a Wedge
- 4.5.1 Estimates of Solutions with DirichletBoundary Condition
- 4.5.2 Estimate on Solutions with Neumann Boundary Condition in the Case dim K>2
- 4.5.3 Estimates of Solutions with Neumann Boundary Condition for dim K=2