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1.

図書

図書
by Viorel Barbu
出版情報: Dordrecht : Kluwer, c1998  xii, 277 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 441
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2.

図書

図書
Lawrence C. Evans
出版情報: Providence, R.I. : American Mathematical Society, c1998  xvii, 662 p. ; 27 cm
シリーズ名: Graduate studies in mathematics ; v. 19
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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
3.

図書

図書
H.O. Fattorini
出版情報: Cambridge : Cambridge University Press, 1999  xv, 798 p. ; 25 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 62
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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

図書
Harold Levine
出版情報: Providence, R.I. : American Mathematical Society , [Cambridge] : International Press, c1997  xviii, 706 p. ; 27 cm
シリーズ名: AMS/IP studies in advanced mathematics ; v. 6
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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
5.

図書

図書
Victor Isakov
出版情報: New York : Springer, c1998  xi, 284 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 127
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6.

図書

図書
Elena Obolashvili
出版情報: Harlow : Longman, 1998  152 p. ; 25 cm
シリーズ名: Pitman monographs and surveys in pure and applied mathematics ; v. 96
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7.

図書

図書
edited by Michael Christ, Carlos E. Kenig, and Cora Sadosky
出版情報: Chicago, Ill. : University of Chicago Press, 1999  xv, 355 p. ; 24 cm
シリーズ名: Chicago lectures in mathematics
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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:
8.

図書

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.:
9.

図書

図書
Joachim Escher, Gieri Simonett editors
出版情報: Basel : Birkhäuser, c1999  ix, 744 p. ; 24 cm
シリーズ名: Progress in nonlinear differential equations and their applications / editor, Haim Brezis ; v. 35
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10.

図書

図書
Luis Caffarelli, Weinan E., editors
出版情報: Providence, R.I. : American Mathematical Society, c1999  xii, 466 p. ; 26 cm
シリーズ名: IAS/Park City mathematics series / [Dan Freed, series editor] ; v. 5
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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)
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