1.
図書
edited by Michael Christ, Carlos E. Kenig, and Cora Sadosky
目次情報:
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Preface
Introduction / Michael Christ ; Carlos E. Kenig ; Cora Sadosky
Calderon and Zygmund's Theory of Singular Integrals / Elias M. Stein1:
Transference Principles in Ergodic Theory / Alexandra Bellow2:
A Weak-Type Inequality for Convolution Products / Alberto P. Calderon3:
Transference Couples and Weighted Maximal Estimates Earl / Berkson ; Maciej Paluszynski ; Guido Weiss4:
Periodic Solutions and Nonlinear Wave Equations / Jean Bourgain5:
Some Extremal Problems in Martingale Theory and Ilarmonic Analysis / Donald L. Burkholder6:
The Monge Ampere Equation, Allocation Problems, and Elliptic Systems with Affine Invariance / Luis A. Caffarelli7:
On a Fourth-Order Partial Differential Equation in Conformal Geometry / Sun-Yung A. Chang8:
Riesz Transforms, Commutators, and Stochastic Integrals / A. B. Cruzeiro ; P. Malliavin9:
An Application of a Formula of Alberto Calderon to Speaker Identification Ingrid / Daubechies ; Stephane Maes10:
Analytic Capacity, Cauchy Kernel, Menger Curvature, and Rectifiability / Guy David11:
Symplectic Subunit Balls and Algebraic Functions / Charles Fefferman12:
Multiparameter Calderon-Zygmund Theory / Robert A. Fefferman13:
Nodal Sets of Sums of Eigenfunctions / David Jerison ; Gilles Lebeau14:
Large-Time Behavior and Self-Similar Solutions of Some Semilinear Diffusion Equations / Yves Meyer15:
Estimates for Elliptic Equations in Unbounded Domains and Applications to Symmetry and Monotonicity / Louis Nirenberg16:
Asymptotic Expansions for Atiyah-Patodi-Singer Problems / Robert Seeley17:
Analysis on Metric Spaces / Stephen Semmes18:
Developments in Inverse Problems since Calderon's Foundational Paper Gunther Uhlmann Remarks Addressed to the Conference / 19:
Contributors
Index
Calderón and Zygmund's Theory of Singular Integrals
Transference Couples and Weighted Maximal Estimates Earl Berkson / Alberto P. Calderón
An Application of a Formula of Alberto Calderón to Speaker Identification / Ingrid Daubechies ; Stéphane Maes
Multiparameter Calderón-Zygmund Theory
Developments in Inverse Problems since Calderón's Foundational Paper Gunther Uhlmann Remarks Addressed to the Conference
Preface
Introduction / Michael Christ ; Carlos E. Kenig ; Cora Sadosky
Calderon and Zygmund's Theory of Singular Integrals / Elias M. Stein1:
2.
図書
Ioannis P. Stavroulakis, Stepan A. Tersian
出版情報:
Singapore ; River Edge, N.J. : World Scientific, c1999 x, 297 p. ; 23 cm
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First-order Partial Differential Equations / 1.:
Introduction
Linear First-order Equations / 2.:
The Cauchy Problem for First-order Quasi-linear Equations / 3.:
General Solutions of Quasi-linear Equations / 4.:
Fully-nonlinear First-order Equations / 5.:
Second-order Partial Differential Equations
Linear equations / 6.:
Classification and Canonical Forms of Equations in Two Independent Variables / 7.:
Classification of Almost-linear Equations in R[superscript n] / 8.:
One-Dimensional Wave Equation
The Wave Equation on the Whole Line. D'Alembert Formula / 9.:
The Wave Equation on the Half-line. Reflection Method / 10.:
Mixed Problem for the Wave Equation / 11.:
Inhomogeneous Wave Equation / 12.:
Conservation of the Energy / 13.:
Weak Derivatives and Weak Solutions / 14.:
One-Dimensional Diffusion Equation
Maximum-minimum Principle for the Diffusion Equation / 15.:
The Diffusion Equation on the Whole Line / 16.:
Diffusion on the Half-line / 17.:
Inhomogeneous Diffusion Equation on the Whole Line / 18.:
Shock Waves and Conservation Laws
Conservation laws / 19.:
Burgers' Equation / 20.:
Weak Solutions. Riemann Problem / 21.:
Discontinuous Solutions of Conservation Laws. Rankine-Hugoniot Condition / 22.:
The Laplace Equation
Harmonic functions. Maximum-minimum Principle / 23.:
Green's Identities / 24.:
Green's Functions / 25.:
Green's Functions for a Half-space and Sphere / 26.:
Harnack's Inequalities and Theorems / 27.:
Fourier Series and Fourier Method for PDEs
Fourier Series / 28.:
Orthonormal Systems. General Fourier series / 29.:
Fourier Method for the Diffusion Equation / 30.:
Fourier Method for the Wave Equation / 31.:
Fourier Method for the Laplace Equation / 32.:
Diffusion and Wave Equations in Higher Dimensions
Diffusion Equation in Three Dimensional Space / 33.:
Fourier Method for the Diffusion Equation in Higher Dimensions / 34.:
Kirchoff's Formula for the Wave Equation. Huygens' Principle / 35.:
Fourier Method for the Wave Equation on the Plane. Nodal Sets / 36.:
References
Answers and Hints to Selected Exercises
Index
First-order Partial Differential Equations / 1.:
Introduction
Linear First-order Equations / 2.:
3.
図書
H.O. Fattorini
目次情報:
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Finite Dimensional Control Problems / Part I:
Calculus of variations and control theory / 1:
Optimal control problems without target conditions / 2:
Abstract minimization problems: the minimum principle for the time optimal problem / 3:
Abstract minimization problems: the minimum principle for general optimal control problems / 4:
Infinite Dimensional Control Problems / Part II:
Differential equations in Banach spaces and semigroup theory / 5:
Abstract minimization problems in Hilbert spaces: applications to hyperbolic control systems / 6:
Abstract minimization problems in Banach spaces: abstract parabolic linear and semilinear equations / 7:
Interpolation and domains of fractional powers / 8:
Linear control systems / 9:
Optimal control problems with state constraints / 10:
Optimal control problems with state constraints: The abstract parabolic case / 11:
Relaxed Controls / Part III:
Spaces of relaxed controls: topology and measure theory / 12:
Relaxed controls in finite dimensional systems: existence theory / 13:
Relaxed controls in infinite dimensional spaces: existence theory / 14:
Finite Dimensional Control Problems / Part I:
Calculus of variations and control theory / 1:
Optimal control problems without target conditions / 2:
4.
図書
by Viorel Barbu
5.
図書
Jean Leray ; [editor, Paul Malliavin]
出版情報:
Berlin : Springer, 1998 , Paris : Société mathématique de France, c1998 3 v. ; 25 cm
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6.
図書
Harold Levine
目次情報:
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Introduction
Partial differentiation Solutions of PDE's and their specification PDE's and related arbitrary functions Particular solutions of PDE's
Similarity solutions
Correctly set problems
Some preliminary aspects of linear first order PDE's
First order PDE's, linear First order nonlinear PDE's
Some technical problems and related PDE's
First order PDE's, general theory
First order PDE's with multiple independent variables
Original detaials of the Fourier approach to boundary value problems
Eigenfunctions and eigenvalues
Eigenfunctions and eigenvalues, continued
Non-orthogonal eigenfunctions
Further example of Fourier style analysis
Inhomogeneous problems
Local heat sources
An inhomogeneous configuration
Other eigenfunction/eigenvalue problems
Uniqueness of solutions
Alternative representations of solutions
Other differential equations and inferences therefrom
Second order ODE's
Boundary value problems and Sturm-Liouville theory
Green's functions and boundary value problems
Green's functions and generalizations PDE's, Green's functions, and integral equations
Singular and infinite range problems
Orthogonality and its ramifications
Fourier expansions: Generalities
Fourier expansions: Varied examples Fourier integrals and transforms
Applications of Fourier transforms
Legendre polynomials and related expansions
Bessel functions and related expansions
Hyperbolic equations
Afterwords
Bibliography
Index
Introduction
Partial differentiation Solutions of PDE's and their specification PDE's and related arbitrary functions Particular solutions of PDE's
Similarity solutions
7.
図書
Lawrence C. Evans
目次情報:
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Introduction
Representation formulas for solutions: Four important linear partial differential equations / Part I:
Nonlinear first-order PDE Other ways to represent solutions
Theory for linear partial differential equations: Sobolev spaces / Part II:
Second-order elliptic equations Second-order elliptic equations
Linear evolution equations
Theory for nonlinear partial differential equations: The calculus of variations / Part III:
Nonvariational techniques Hamilton-Jacobi equations
Systems of conservation laws
Appendices
Bibliography
Index
Introduction
Representation formulas for solutions: Four important linear partial differential equations / Part I:
Nonlinear first-order PDE Other ways to represent solutions
8.
図書
J. David Logan
9.
図書
Joachim Escher, Gieri Simonett editors
10.
図書
Elena Obolashvili
11.
図書
M.V. Fedoryuk (ed.)
12.
図書
Kazuaki Taira
13.
図書
Victor Isakov
14.
図書
Heinrich G.W. Begehr and Abduhamid Dzhuraev
15.
図書
M.S. Agranovich, Yu.V. Egorov and M.A. Shubin (eds.)
目次情報:
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Preface
Legal Matters
Introduction
Background on Probability and Statistics
Stochastic Differential Equations
Introduction to Discrete Time Approximation
Strong Approximations
Weak Approximations
Applications
References Subject
Index
List of PC-Exercises
Frequently Used Notations
Preface
Legal Matters
Introduction
16.
図書
Emmanuele DiBenedetto
出版情報:
Boston : Birkhäuser, 1995 xiv, 416 p. ; 25 cm
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17.
図書
Jean Cea ... [et al.], editors
18.
図書
Vladislav V. Kravchenko and Michael V. Shapiro
19.
図書
edited by Paolo Marcellini, Giorgio Talenti, Edoardo Vesentini
目次情報:
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Spatial decay estimates for an evolution equation
on the range of Ural'tseva's axially symmetric operator in Sobolev spaces
the use of a priori information in the solution of ill-posed problems
allocation maps with general cost functions
an elementary theorem in plane geometry and its multidimensional extension
minimum problems for volumes of convex bodies
on the continuous dependence of the solution of a linear parabolic partial differential equation on the boundary data and the
Spatial decay estimates for an evolution equation
on the range of Ural'tseva's axially symmetric operator in Sobolev spaces
the use of a priori information in the solution of ill-posed problems
20.
図書
Gerald B. Folland
出版情報:
Princeton, N.J. : Princeton University Press, c1995 xi, 324 p. ; 24 cm
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21.
図書
M.A. Shubin (ed.)
22.
図書
John H. Hubbard, Beverly H. West
23.
図書
Willi-Hans Steeb
出版情報:
Singapore : World Scientific, c1996 xi, 360 p. ; 23 cm
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24.
図書
by Zofia Szmydt and Bogdan Ziemian
25.
図書
V.V. Zharinov
26.
図書
Dominic G.B. Edelen & Jian-hua Wang
出版情報:
Singapore ; New Jersey : World Scientific, c1992 xii, 325 p. ; 23 cm
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27.
図書
L.A. Dickey
28.
図書
Yu.V. Egorov, M.A. Shubin (eds.)
目次情報:
The Cauchy problem / S.G. Gindikin, L.R. Volevich
Qualitative theory of second order linear partial differential equations / V.A. Kondratʹev, E.M. Landis
The Cauchy problem / S.G. Gindikin, L.R. Volevich
Qualitative theory of second order linear partial differential equations / V.A. Kondratʹev, E.M. Landis
29.
図書
Heinrich Begehr and Robert P. Gilbert
30.
図書
by S. Gindikin and L.R. Volevich
31.
図書
François Treves
32.
図書
Guangchang Dong
目次情報:
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The first boundary value problem for second-order quasilinear parabolic equations with principal part in divergence form
A periodic boundary value problem for a nonlinear telegraph equation
The initial value problem for a nonlinear Schrodinger equation
Multi-dimensional subsonic flows around an obstacle
The initial-boundary value problem for degenerate quasilinear parabolic equations
The speed of propagation of the solution of a degenerate quasilinear parabolic equation
Aleksandrov and Bony maximum principles for parabolic equations
The density theorem and its applications
Fully nonlinear parabolic equations
Fully nonlinear parabolic equations (continued)
The first boundary value problem for second-order quasilinear parabolic equations with principal part in divergence form
A periodic boundary value problem for a nonlinear telegraph equation
The initial value problem for a nonlinear Schrodinger equation
33.
図書
Yu.V. Egorov, M.A. Shubin (eds.)
34.
図書
Jeffrey Rauch
目次情報:
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Power Series Methods
Some Harmonic Analysis
Solution of Initial Value Problems by Fourier Synthesis
Propagators and x-Space Methods
The Dirichlet Problem
Appendix: A Crash Course in Distribution Theory
References
Index
Power Series Methods
Some Harmonic Analysis
Solution of Initial Value Problems by Fourier Synthesis
35.
図書
B.D. Sleeman and R.J. Jarvis, editors
36.
図書
A.V. Babin, M.I. Vishik, editors
目次情報:
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Asymptotic expansion at infinity of a strongly perturbed Poiseuille flow / A. V. Babin
Unbounded attractors of evolution equations / V. V. Chepyzhov ; A. Yu. Goritskii
Attractors of singularly perturbed parabolic equations, and asymptotic behavior of their elements / M. Yu. Skvortsov ; M. I. Vishik
The asymptotics of solutions of reaction-diffusion equations with small parameter / V. Yu. Skvortsov
Asymptotic expansion at infinity of a strongly perturbed Poiseuille flow / A. V. Babin
Unbounded attractors of evolution equations / V. V. Chepyzhov ; A. Yu. Goritskii
Attractors of singularly perturbed parabolic equations, and asymptotic behavior of their elements / M. Yu. Skvortsov ; M. I. Vishik
37.
図書
Elemér E. Rosinger
出版情報:
Amsterdam ; Tokyo : North-Holland , New York, N.Y. : Distributors for the United States and Canada, Elsevier Science Pub, 1990 xxi, 380 p. ; 25 cm
シリーズ名:
North-Holland mathematics studies ; 164
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38.
図書
Daniel D. Joseph
39.
図書
by V.I. Gorbachuk and M.L. Gorbachuk
40.
図書
R.L. Bryant ... [et al.]
41.
図書
N. Asano and Y. Kato
42.
図書
John H. Hubbard, Beverly H. West
目次情報:
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Series Preface for Texts in Applied Mathematics Preface Acknowledgments Ways to Use This Book Introduction
Qualitative Methods / Chapter 1:
Fields of Slopes and Sketching of Solutions / 1.1:
Qualitative Description of Solutions / 1.2:
Fences / 1.3:
Funnels and Antifunnels / 1.4:
The Use of Fences, Funnels, and Antifunnels Exercises / 1.5:
Analystic Methods / Chapter 2:
Separation of Variables / 2.1:
Linear Differential Equations of First Order / 2.2:
Variation of Parameters / 2.3:
Bank Accounts and Linear Differential Equations / 2.4:
Series Preface for Texts in Applied Mathematics Preface Acknowledgments Ways to Use This Book Introduction
Qualitative Methods / Chapter 1:
Fields of Slopes and Sketching of Solutions / 1.1:
43.
図書
John M. Rassias
出版情報:
Singapore : World Scientific, c1990 vii, 144 p. ; 23 cm
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44.
図書
Victor Isakov
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Preliminaries Results overlook
Uniqueness theorems
Singular points of the exterior potential
Existence theory
Parabolic problems
Hyperbolic problems
Preliminaries Results overlook
Uniqueness theorems
Singular points of the exterior potential
45.
図書
Lars Hörmander
46.
図書
J. Kevorkian
目次情報:
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Preface
The Diffusion Equation
Laplace's Equation
The Wave Equation
Linear Second-Order Equations with Two Independent Variables
The Scalar Quasilinear First-Order Equation
Nonlinear First-Order Equations
Quasilinear Hyperbolic Systems
Approximate Solutions by Perturbation Methods
Appendix
References
Index
Preface
The Diffusion Equation
Laplace's Equation
47.
図書
edited by Boris A. Kupershmidt
出版情報:
Singapore : World Scientific, c1990 viii, 388 p. ; 23 cm
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48.
図書
Lars Hörmander
出版情報:
Amsterdam ; New York ; Tokyo : North-Holland , New York, N.Y. : Distributors for the United States and Canada, Elsevier Science, 1990 xii, 254 p. ; 23 cm
シリーズ名:
North-Holland mathematical library ; v. 7
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Analytic Functions of One Complex Variable / I:
Elementary Properties of Functions of Several Complex Variables / II:
Applications to Commutative Banach Algebras / III:
L 2 Estimates and Existence Theorems for the Operator / IV:
Stein Manifolds / V:
Local Properties of Analytic Functions / VI:
Coherent Analytic Sheaves on Stein Manifolds / VII:
Bibliography
Index
Analytic Functions of One Complex Variable / I:
Elementary Properties of Functions of Several Complex Variables / II:
Applications to Commutative Banach Algebras / III:
49.
図書
edited by Gary D. Doolen ... [et al.]
50.
図書
G.M. Khenkin (ed.)
51.
図書
A.V. Bitsadze
52.
図書
Otto Liess
53.
図書
Yu.V. Egorov, M.A. Shubin (eds.)
目次情報:
Linear Partial Differential Equations
Elements of Modern Theory / Yu.V. Egorov ; M.A. Shubin
Linear Partial Differential Equations with Constant Coefficients / A.I. Komech
Linear Partial Differential Equations
Elements of Modern Theory / Yu.V. Egorov ; M.A. Shubin
Linear Partial Differential Equations with Constant Coefficients / A.I. Komech
54.
図書
M.A. Shubin (ed.)
目次情報:
Spectral Theory of Differential Operators / G.V. Rozenblum ; M.A. Shubin ; M.Z. Solomyak
Spectral Theory of Differential Operators / G.V. Rozenblum ; M.A. Shubin ; M.Z. Solomyak
55.
図書
by Boris Sternin and Victor Shatalov
56.
図書
J. David Logan
57.
図書
by J.-F. Pommaret
58.
図書
Yu.V. Egorov, M.A. Shubin (eds.)
目次情報:
Elliptic Operators on Closed Manifolds / M.S.Agranovich
Degenerate Elliptic Equations and Boundary Problems / S.Z.Levendorskij ; B.Paneah
Parabolic Equations / S.D.Ejdel'man
Elliptic Operators on Closed Manifolds / M.S.Agranovich
Degenerate Elliptic Equations and Boundary Problems / S.Z.Levendorskij ; B.Paneah
Parabolic Equations / S.D.Ejdel'man
59.
図書
Michael Renardy, Robert C. Rogers
60.
図書
Peter Kuchment
61.
図書
Michael E. Taylor
目次情報:
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Volumes II and III
Introduction
Basic Theory of ODE and Vector Fields
The Laplace Equation and Wave Equation
Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE
Sobolev Spaces
Linear Elliptic Equations
Linear Evolution Equations
Outline of Functional Analysis / Appendix A:
Manifolds, Vector Bundles, and Lie Groups / Appendix B:
Index
Volumes II and III
Introduction
Basic Theory of ODE and Vector Fields
62.
図書
Michael E. Taylor
目次情報:
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Volumes I and III
Introduction
Pseudodifferential Operators
Spectral Theory
Scattering by Obstacles
Dirac Operators and Index Theory
Brownian Motion and Potential Theory
The Partial-Neumann Problem
Connections and Curvature
Index
Volumes I and III
Introduction
Pseudodifferential Operators
63.
図書
Michael E. Taylor
目次情報:
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Function space and operator theory for nonlinear analysis / 13:
Nonlinear elliptic equations / 14:
Nonlinear parabolic equations / 15:
Nonlinear hyperbolic equations / 16:
Euler and Navier-Stokes equations for incompressible fluids / 17:
Einstein's equations / 18:
Function space and operator theory for nonlinear analysis / 13:
Nonlinear elliptic equations / 14:
Nonlinear parabolic equations / 15:
64.
図書
Hiroki Tanabe
65.
図書
Prem K. Kythe, Pratap Puri, Michael R. Schäferkotter
出版情報:
Boca Raton, Fla. ; Tokyo : CRC Press, c1997 xx, 378 p. ; 24 cm
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66.
図書
A.A. Melikyan
出版情報:
Boston : Birkhäuser, 1998 xiv, 310 p. ; 24 cm
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67.
図書
Luis Caffarelli, Weinan E., editors
目次情報:
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Nonlinear Schrodinger equations: Introduction / J. Bourgain
Generalities and initial value problems
The initial value problem (continued)
A digressioin: The initial value problem for the KdV equation
1D invariant Gibbs measures
Invariant measures (2D)
Quasi-periodic solutions of Hamiltonian PDE
Time periodic solutions
Time quasi-periodic solutions
Normal forms
Applications of symplectic capacities to Hamiltonian PDE
Remarks on longtime behaviour of the flow of Hamiltonian PDE
Harmonic analysis, wavelets and applications: Introduction / I. C. Daubechies ; A. C. Gilbert
Constructing orthonormal wavelet bases: Multiresolution analysis
Wavelet bases: Construction and algorithms
More wavelet bases
Wavelets in other functional spaces
Pointwise convergence for wavelet expansions
Two-dimensional wavelets and operators
Wavelets and differential equations
References
Lectures on stability and instability of an ideal fluid: Introduction / S. Friedlander
Equations of motion
Initial-boundary value problem
The type of the Euler equations
Vorticity
Steady flows
Stability/instability of an equilibrium state
Two-dimensional spectral problem
"Arnold" criterion for nonlinear stability
Plane parallel shear flow
Instability in a vorticity norm
Sufficient condition for instability
Exponential stretching
Integrable flows
Baroclinic instability
Nonlinear instability
Waves and transport: Introduction / G. Papanicolaou ; L. Ryzhik
The Schrodinger equation
Symmetric hyperbolic systems
Waves in random media
The diffusion approximation
The geophysical applications
Lectures on geometric optics: Introduction / J. Rauch ; M. Keel
Basic linear existence theorems
Examples of propagation of singularities and of energy
Elliptic geometric optics
Linear hyperbolic geometric optics
Basic nonlinear existence theorems
One phase nonlinear geometric optics
Justification of one phase nonlinear geometric optics
Nonlinear Schrodinger equations: Introduction / J. Bourgain
Generalities and initial value problems
The initial value problem (continued)
68.
図書
J. Málek ... [et al.]
69.
図書
Geoff Stephenson
出版情報:
London : Imperial College Press, 1996 x, 161 p. ; 22 cm
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