Singular Perturbations and Boundary Layers. ([2018])
- Record Type:
- Book
- Title:
- Singular Perturbations and Boundary Layers. ([2018])
- Main Title:
- Singular Perturbations and Boundary Layers
- Further Information:
- Note: Gung-Min Gie [and others].
- Authors:
- Gie, Gung-Min
- Contents:
- Intro; Preface; Contents; List of Symbols and Abbreviations; 1 Singular Perturbations in Dimension One; 1.1 Introduction; 1.2 Regular and Singular Perturbations; 1.3 Reaction-Diffusion Equations in 1D; 1.3.1 Convergence by Energy Methods; 1.3.2 Thickness of the Boundary Layer and the Boundary Layer Correctors; 1.3.3 Inner and Outer Expansions: The Higher Orders; 1.3.4 Higher Order Regularity and Convergence; 1.4 Convection-Diffusion Equations in 1D; 1.4.1 Asymptotic Expansions at Order n, n ≥0; 1.4.2 Higher Order Regularity and Convergence; 1.4.3 Problem with a Variable Coefficient b(x) 2 Singular Perturbations in Higher Dimensions in a Channel2.1 Introduction; 2.2 Reaction-Diffusion Equations in a Channel: Ordinary Boundary Layers; 2.2.1 Energy Method; 2.2.2 Boundary Layer Analysis; 2.2.3 Outer and Inner Expansions; 2.2.4 Some Lemmas; 2.2.5 Outer and Inner Expansions (Continued); 2.2.6 Higher Order Regularity and Convergence; 2.3 Convection-Diffusion Equations in a Channel: Parabolic Boundary Layers; 2.3.1 Convection-Diffusion Equations in Higher Dimensions; 2.3.2 Introduction of the Parabolic Boundary Layers (PBL); 2.3.3 Outer Expansions; 2.3.4 PBL at Order 0: 0, 2.3.5 Inner Expansions2.3.5.1 PBL at Order j: j, , j ≥1; 2.3.5.2 Estimates on the PBLs; 2.3.6 The Approximation Results; 2.3.7 Higher Order Regularity and Convergence; 3 Boundary Layers in a Curved Domain in Rd, d = 2, 3; 3.1 Elements of Differential Geometry; 3.1.1 A Curvilinear Coordinate System Adapted to theIntro; Preface; Contents; List of Symbols and Abbreviations; 1 Singular Perturbations in Dimension One; 1.1 Introduction; 1.2 Regular and Singular Perturbations; 1.3 Reaction-Diffusion Equations in 1D; 1.3.1 Convergence by Energy Methods; 1.3.2 Thickness of the Boundary Layer and the Boundary Layer Correctors; 1.3.3 Inner and Outer Expansions: The Higher Orders; 1.3.4 Higher Order Regularity and Convergence; 1.4 Convection-Diffusion Equations in 1D; 1.4.1 Asymptotic Expansions at Order n, n ≥0; 1.4.2 Higher Order Regularity and Convergence; 1.4.3 Problem with a Variable Coefficient b(x) 2 Singular Perturbations in Higher Dimensions in a Channel2.1 Introduction; 2.2 Reaction-Diffusion Equations in a Channel: Ordinary Boundary Layers; 2.2.1 Energy Method; 2.2.2 Boundary Layer Analysis; 2.2.3 Outer and Inner Expansions; 2.2.4 Some Lemmas; 2.2.5 Outer and Inner Expansions (Continued); 2.2.6 Higher Order Regularity and Convergence; 2.3 Convection-Diffusion Equations in a Channel: Parabolic Boundary Layers; 2.3.1 Convection-Diffusion Equations in Higher Dimensions; 2.3.2 Introduction of the Parabolic Boundary Layers (PBL); 2.3.3 Outer Expansions; 2.3.4 PBL at Order 0: 0, 2.3.5 Inner Expansions2.3.5.1 PBL at Order j: j, , j ≥1; 2.3.5.2 Estimates on the PBLs; 2.3.6 The Approximation Results; 2.3.7 Higher Order Regularity and Convergence; 3 Boundary Layers in a Curved Domain in Rd, d = 2, 3; 3.1 Elements of Differential Geometry; 3.1.1 A Curvilinear Coordinate System Adapted to the Boundary; 3.1.2 Examples of the Curvilinear System for Some Special Geometries; 3.2 Reaction-Diffusion Equations in a Curved Domain; 3.2.1 Boundary Layer Analysis at Order 0; 3.2.2 Boundary Layer Analysis at Order 1/2: The Effect of the Curvature 3.2.3 Asymptotic Expansions at Arbitrary Orders n and n+1/2, n ≥03.3 Parabolic Equations in a Curved Domain; 3.3.1 Boundary Layer Analysis at Orders 0 and 1/2; 3.3.2 Boundary Layer Analysis at Arbitrary Orders n and n+1/2, n ≥0; 3.3.3 Analysis of the Initial Layer: The Case of Ill-Prepared Initial Data; 4 Corner Layers and Turning Points for Convection-Diffusion Equations; 4.1 Convection-Diffusion Equations in a Rectangular Domain; 4.1.1 The Zeroth Order 0; 4.1.1.1 Parabolic Boundary Layers (PBL); 4.1.1.2 Ordinary Boundary Layers (OBL); 4.1.1.3 Ordinary Corner Layers (OCL) 4.1.1.4 Convergence Theorem4.1.2 The Higher Orders n, n≥1; 4.1.2.1 Parabolic Boundary Layers (PBL) Near y=0; 4.1.2.2 Elliptic Boundary Layers (EBL) Near y = 0 and x=1; 4.1.2.3 Ordinary Boundary Layers (OBL) Near x=0; 4.1.2.4 Ordinary Corner Layers (OCL) Near y=0 and x=0; 4.1.2.5 Elliptic Corner Layers (ECL) Near y=0 and x=0; 4.1.2.6 Convergence Theorem; 4.2 Convection-Diffusion Equations in a Bounded Interval with a Turning Point; 4.2.1 The Outer Expansion; 4.2.2 Definition of the Correctors at All Orders; 4.2.3 The Case of f, b Compatible; 4.2.4 The Case of f, b Noncompatible … (more)
- Publisher Details:
- Cham, Switzerland : Springer
- Publication Date:
- 2018
- Copyright Date:
- 2018
- Extent:
- 1 online resource
- Subjects:
- 510
Boundary layer
Differential equations, Partial
Singular perturbations (Mathematics)
MATHEMATICS / Essays
MATHEMATICS / Pre-Calculus
MATHEMATICS / Reference
Functional Analysis
Approximations and Expansions
Boundary layer
Differential equations, Partial
Singular perturbations (Mathematics)
Electronic books - Languages:
- English
- ISBNs:
- 9783030006389
3030006387 - Related ISBNs:
- 9783030006372
- Notes:
- Note: Includes bibliographical references and index.
Note: Online resource; title from PDF title page (EBSCO, viewed November 30, 2018). - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
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- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.377977
- Ingest File:
- 02_359.xml