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Integral Equation Methods in Scattering Theory [Pehme köide]

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  • Formaat: Paperback, 287 pages, kõrgus x laius x paksus: 229x152x15 mm, kaal: 400 g, illustrations
  • Sari: Classics in Applied Mathematics
  • Ilmumisaeg: 30-Nov-2013
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611973155
  • ISBN-13: 9781611973150
Teised raamatud teemal:
Integral Equation Methods in Scattering TheorySuurem pilt
  • Formaat: Paperback, 287 pages, kõrgus x laius x paksus: 229x152x15 mm, kaal: 400 g, illustrations
  • Sari: Classics in Applied Mathematics
  • Ilmumisaeg: 30-Nov-2013
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611973155
  • ISBN-13: 9781611973150
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781611973150.html
This classic book provides a rigorous treatment of the Riesz-Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and Holder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from:* A full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and Holder continuous functions.* An in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves.* An introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.
Preface to the Classics Edition xi
Preface xiii
Symbols xv
1 The Riesz--Fredholm Theory for Compact Operators
1(30)
1.1 Compact Operators
2(7)
1.2 The Riesz Theory
9(7)
1.3 The Fredholm Theory
16(7)
1.4 A Singular Perturbation Problem
23(3)
1.5 Successive Approximations
26(5)
2 Regularity Properties of Surface Potentials
31(34)
2.1 Geometry of Surfaces
32(5)
2.2 Holder Continuity
37(2)
2.3 Weakly Singular Integral Operators on Surfaces
39(7)
2.4 Single- and Double-Layer Potentials
46(5)
2.5 Derivatives of Single- and Double-Layer Potentials
51(7)
2.6 Vector Potentials
58(3)
2.7 Integral Operators for Boundary-Value Problems
61(4)
3 Boundary-Value Problems for the Scalar Helmholtz Equation
65(43)
3.1 Time-Harmonic Acoustic Scattering
66(2)
3.2 Green's Representation Theorem and Sommerfeld's Radiation Condition
68(7)
3.3 The Dirichlet and Neumann Boundary-Value Problems: Uniqueness Theorems
75(4)
3.4 The Existence of Solutions to the Dirichlet and Neumann Problems
79(8)
3.5 Boundary Integral Equations of the First Kind
87(3)
3.6 Modified Integral Equations
90(7)
3.7 The Impedance Boundary-Value Problem
97(2)
3.8 The Transmission Boundary-Value Problem
99(3)
3.9 Integral Equations Based on the Representation Theorems
102(4)
3.10 The Two-Dimensional Case
106(2)
4 Boundary-Value Problems for the Time-Harmonic Maxwell Equations and the Vector Helmholtz Equation
108(42)
4.1 Time-Harmonic Electromagnetic Scattering
109(1)
4.2 Representation Theorems and Radiation Conditions
110(11)
4.3 The Boundary-Value Problems for a Perfect Conductor: Uniqueness Theorems
121(5)
4.4 Existence of Solutions to the Electromagnetic Boundary-Value Problems by Integral Equations of the Second Kind
126(10)
4.5 Boundary Integral Equations of the First Kind
136(4)
4.6 Modified Integral Equations
140(6)
4.7 The Impedance Boundary-Value Problem
146(1)
4.8 Integral Equations Based on the Representation Theorems
147(3)
5 Low Frequency Behavior of Solutions to Boundary-Value Problems in Scattering Theory
150(23)
5.1 Iterative Methods for Solving the Exterior Dirichlet and Neumann Problems
151(3)
5.2 Iterative Methods for Electromagnetic Problems
154(4)
5.3 Low Wave Number Behavior of Solutions to the Exterior Electromagnetic Boundary-Value Problems
158(15)
6 The Inverse Scattering Problem: Exact Data
173(24)
6.1 Entire Functions of Exponential Type
175(7)
6.2 Far-Field Patterns and Their Classification
182(10)
6.3 Uniqueness of Solutions to the Inverse Scattering Problem
192(5)
7 Improperly Posed Problems and Compact Families
197(22)
7.1 A Priori Assumptions and the Solution of Improperly Posed Problems
198(8)
7.2 Linearized Improperly Posed Problems in Scattering Theory
206(5)
7.3 Normal Families of Univalent Functions
211(8)
8 The Determination of the Shape of an Obstacle from Inexact Far-Field Data
219(25)
8.1 A Model Problem
221(11)
8.2 The Determination of the Shape of an Obstacle in R2
232(7)
8.3 The Determination of the Shape of an Obstacle in R3
239(5)
9 Optimal Control Problems in Radiation and Scattering Theory
244(17)
9.1 Weak Compactness in Hilbert Space
245(2)
9.2 Optimal Control for a Radiation Problem
247(7)
9.3 Optimal Control for a Scattering Problem
254(7)
References 261(8)
Index 269
David Colton is Unidel Professor of Mathematics at the University of Delaware. He is the author or coauthor of six books, including The Linear Sampling Method in Inverse Electromagnetic Scattering (2011), written with Fioralba Cakoni and Peter Monk. Rainer Kress is a Full Professor of Numerical and Applied Mathematics at the University of Gottingen. He has been a member of the Gottingen Academy of Sciences since 1995 and Professor Emeritus since 2010. He is the author or coauthor of five books.