Asymptotic theory of dynamic boundary value problems in irregular domains / Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov.
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Ebook |
| Language: | English |
| Published: |
Cham :
Birkhäuser,
[2021]
|
| Series: | Operator theory, advances and applications ;
v. 284. |
| Subjects: | |
| Online Access: | Springer eBooks |
Table of Contents:
- Introduction
- Wave Equation in Domains with Edges
- Dirichlet Problem for the Wave Equation
- Function Spaces in a Wedge and in a Cone
- Problem in a Wedge : Problem with Parameter in a Cone : Existence of Solutions
- Weighted Combined Estimates
- Operators in the Scale of Weighted Spaces
- Asymptotics of Solutions Near the Vertex of a Cone or Near the Edge of a Wedge
- Explicit Formulas for the Coefficients in Asymptotics
- Problem in a Bounded Domain with Conical Points
- Problem in a Bounded Domain : Asymptotics of Solutions Near an Internal Point
- Neumann Problem for the Wave Equation
- Statement of the Problem : Preliminaries
- Weighted Combined Estimates for Solutions to Problem (2.138), (2.139)
- Operator of the Boundary Value Problem in a Cone
- Boundary Value Problem in a Cone in the Scale of Weighted Spaces
- Asymptotic Expansions of Solutions to the Problem in a Cone
- Problem in a Wedge
- Explicit Formulas for the Coefficients in Asymptotics
- Problem in a Bounded Domain with Conical Points
- Hyperbolic Systems in Domains with Conical Points
- Cauchy-Dirichlet Problem
- Combined Estimate for Solutions of the Problem in a Cone
- Operator of the Boundary Value Problem in a Cone : The Existence and Uniqueness of Solutions
- The Boundary Value Problem in a Cone in the Scale of Weighted Spaces
- Asymptotics of Solutions of the Problem in a Cone
- The Problem in a Wedge
- Neumann Problem
- The Model Problems in a Cone : A Strong Solution
- Weighted Estimates of Solutions of the Problem with Parameter in a Cone
- The Problem with Parameter in a Cone : A Scale of Weighted Spaces
- The Asymptotics of Solutions
- A Bounded Domain with a Conical Point
- Elastodynamics in Domains with Edges
- Introduction
- Homogeneous Energy Estimates on Solutions of Boundary Value Problems with Parameter in a Wedge
- Nonhomogeneous Energy Estimates for Solutions of Boundary Value Problems with Parameter in a Wedge
- Estimates on Solutions with Dirichlet Boundary Condition
- Estimates on Solutions with Neumann Boundary Condition
- Strong Solutions
- The Dirichlet Problem with Homogeneous Energy Estimate in a Wedge
- The Dirichlet Problem with Nonhomogeneous Energy Estimate in a Wedge
- The Neumann Problem in a Wedge
- Weighted a priori Estimates for Solutions of Boundary Value Problems with Parameter in a Wedge
- Estimates of Solutions with Dirichlet Boundary Condition
- Estimate on Solutions with Neumann Boundary Condition in the Case dimK > 2
- Estimates of Solutions with Neumann Boundary Condition for dimK=2
- Boundary Value Problem in a Cone in a Scale of Weighted Spaces
- On the Asymptotics of Solutions of Elliptic Problems in a Cone
- Strong Solutions
- The Operator of Problem (4.105), (4.106) in a Scale of Weighted Spaces
- Asymptotics of Solutions of the Problem in a Cone
- On the Time-Dependent Problem in a Wedge
- Energy Estimates on Solutions in a Bounded Domain
- Weighted Estimates in a Bounded Domain with Edge
- On Dynamic Maxwell System in Domains with Edges
- The Problems in a Cone and in a Bounded Domain with Conical Point
- Preliminaries : Statement of the Problem
- Operator Pencil
- A Global Energy Estimate
- A Combined Weighted Estimate
- The Operator of Problem in a Scale of Weighted Spaces
- The Asymptotics of Solutions
- Nonstationary Problem in the Cylinders ... and Q
- Explicit Formulas of ws, k and Ws, k for the Problem in K
- The Problem in a Wedge
- Preliminaries : Statement of the Problem
- Operator Pencil
- On Properties of the Operator A(D)
- Estimates of Solutions to Problems in a Wedge and in an Angle
- The Operators of Problems in K
- The Problem in the Cylinder T
- Explicit Formulas for the Coefficients in the Asymptotics of Solutions of the Problem in T
- Connection Between the Augmented and Non-augmented Maxwell Systems
- Schroedinger and Germain-Lagrange Equations in a Domain with Corners
- Schroedinger Equation
- Germain-Lagrange Equation with Simply Supported Boundary Conditions
- Combined Estimates
- Asymptotics of Solutions
- Germain-Lagrange Equation with Clamped Boundary Conditions
- Problem in the Wedge : Problem with Parameter in a Sector-Existence of Solutions
- Weighted Combined Estimates
- Operators in the Scale of Weighted Spaces
- Asymptotics of Solutions
- Problem in a Bounded Domain with Corners
- Asymptotics of Solutions to Wave Equation in Singularly Perturbed Domains
- Asymptotics of Solutions to Wave Equation in a Domain with Small Cavity
- Statement of Problem : Principal Term of Asymptotics
- Estimate of the Remainder
- Full Asymptotic Expansion
- Asymptotics of Solutions to Wave Equation in a Domain with "Smoothed" Conical Point
- Asymptotics of Solutions to Non-stationary Maxwell System in a Domain with Small Cavities
- Elliptic Extension of Maxwell System with Parameter ...
- Operator Pencil
- The First Limit Problem
- The Second Limit Problem
- Asymptotics Principal Term of Solution to Extended Problem
- Asymptotic Series for Solution to Extended Problem
- Asymptotics for Solutions to Non-extended Maxwell System
- Non-stationary Maxwell System
- Statement of Problem
- Preliminary Description of Asymptotics for Solutions to Extended Problem
- Principal Term of Asymptotics for Solutions to Problem (8.111), (8.112)
- Proof of Theorem 8.7.4
- Estimate of the Remainder ũ₁(·, ...) for ...
- Estimate of the Functions u(·, ...) and u₀(·, ...) for ...
- Return to Extended Hyperbolic Problem
- Return to Non-stationary Maxwell System Under Compatibility Conditions
- Asymptotic Series as ... 0 for Solutions to Hyperbolic Problem
- Estimates of Coefficients and Remainders in (8.88), (8.89)
- Estimate, Uniform with Respect to ..., of the Remainder ũN+1(·, ...) in the Expansion (8.100)
- Return to Non-extended Maxwell System (8.1) in (8.100), (8.101)
- Complete Asymptotic Expansion of Solutions to Problem (8.111), (8.112)
- Stationary Maxwell System with Impedance Boundary Conditions
- Asymptotics for Solutions to Problem (8.192), (8.193)
- Principal Term of Asymptotics
- Estimate of the Remainder
- Complete Asymptotic Expansion
- Return to the Non-extended Maxwell System
- Non-stationary Maxwell System with Impedance Boundary Conditions
- Generalization to the Case of a Domain with Several Small Cavities
- Bibliographical Sketch
- References.