close
1.

図書
図書
1. Introduction to PDEs and waves for the atmosphere and ocean (: pbk.)
Andrew Majda
出版情報: New York : Courant Institute of Mathematical Sciences, New York University , Providence, R.I : American Mathematical Society, 2003  ix, 234 p. ; 26 cm
シリーズ名: Courant lecture notes in mathematics ; 9
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / Chapter 1.：
Basic Properties of the Equations with Rotation and Stratification / 1.1.：
Two-Dimensional Exact Solutions / 1.2.：
Buoyancy and Stratification / 1.3.：
Jet Flows with Rotation and Stratification / 1.4.：
From Vertical Stratification to Shallow Water / 1.5.：
Some Remarkable Features of Stratified Flow / Chapter 2.：
Energy Principle / 2.1.：
Vorticity in Stratified Fluids and Exact Solutions Motivated by Local Analysis / 2.2.：
Use of Theorem 2.4: Exact Two-Dimensional Solutions / 2.3.：
Nonlinear Plane Waves in Stratified Flow: Internal Gravity Waves / 2.4.：
Exact Solutions with Large-Scale Motion and Nonlinear Plane Waves / 2.5.：
More Details for Theorem 2.7 on Special Exact Solutions for the Boussinesq Equations Including Plane Waves / 2.6.：
Linear and Nonlinear Instability of Stratified Flows with Strong Stratification / Chapter 3.：
Boussinesq Equations and Vorticity Stream Formulation / 3.1.：
Nonlinear Instability of Stratified Flows / 3.2.：
Shear Flows / 3.3.：
Some Background Facts on ODEs / 3.4.：
Rotating Shallow Water Theory / Chapter 4.：
Rotating Shallow Water Equations / 4.1.：
Conservation of Potential Vorticity / 4.2.：
Nonlinear Conservation of Energy / 4.3.：
Linear Theory for the Rotating Shallow Water Equations / 4.4.：
Nondimensional Form of the Rotating Shallow Water Equations / 4.5.：
Derivation of the Quasi-Geostrophic Equations / 4.6.：
The Quasi-Geostrophic Equations as a Singular PDE Limit / 4.7.：
The Model Rotating Shallow Water Equations / 4.8.：
Preliminary Mathematical Considerations / 4.9.：
Regorous Convergence of the Model Rotating Shallow Water Equations to the Quasi-Geostrophic Equations / 4.10.：
Proof of the Convergence Theorem / 4.11.：
Linear and Weakly Nonlinear Theory of Dispersive Waves with Geophysical Examples / Chapter 5.：
Linear Wave Midlatitude Planetary Equations / 5.1.：
Dispersive Waves: General Properties / 5.2.：
Interpretation of Group Velocity / 5.3.：
Distant Propagation from a Localized Source / 5.4.：
WKB Methods for Linear Dispersive Waves / 5.5.：
Beyond Caustics: Eikonal Equation Revisited / 5.6.：
Weakly Nonlinear WKB for Perturbations Around a Constant State / 5.7.：
Nonlinear WKB and the Boussinesq Equations / 5.8.：
Simplified Equations for the Dynamics of Strongly Stratified Flow / Chapter 6.：
Nondimensionalization of the Boussinesq Equations for Stably Stratified Flow / 6.1.：
The Vorticity Stream Formulation and Elementary Properties of the Limit Equations for Strongly Stratified Flow / 6.2.：
Solutions of the Limit Dynamics with Strong Stratification as Models for Laboratory Experiments / 6.3.：
The Stratified Quasi-Geostrophic Equations as a Singular Limit of the Rotating Boussinesq Equations / Chapter 7.：
The Rotating Boussinesq Equations / 7.1.：
The Nondimensional Rotating Boussinesq Equations / 7.3.：
Formal Asymptotic Derivation of the Quasi-Geostrophic Equations as a Distinguished Asymptotic Limit of Small Rossby and Froude Numbers / 7.4.：
Rigorous Convergence of the Rotating Boussinesq Equations to the Quasi-Geostrophic Equations / 7.5.：
Introduction to Averaging over Fast Waves for Geophysical Flows / 7.6.：
Motivation for Fast-Wave Averaging / 8.1.：
A General Framework for Averaging over Fast Waves / 8.3.：
Elementary Analytic Models for Comparing Instabilities at Low Froude Numbers with the Low Froude Number Limit Dynamics / 8.4.：
The Rapidly Rotating Shallow Water Equations with Unbalanced Initial Data in the Quasi-Geostrophic Limit / 8.5.：
The Interaction of Fast Waves and Slow Dynamics in the Rotating Stratified Boussinesq Equations / 8.6.：
Waves and PDEs for the Equatorial Atmosphere and Ocean / Chapter 9.：
Introduction to Equatorial Waves for Rotating Shallow Water / 9.1.：
The Equatorial Primitive Equations / 9.2.：
The Nonlinear Equatorial Long-Wave Equations / 9.3.：
A Simple Model for the Steady Circulation of the Equatorial Atmosphere / 9.4.：
Bibliography
Preface
Introduction / Chapter 1.：
Basic Properties of the Equations with Rotation and Stratification / 1.1.：
2.

図書
図書
2. Abstract parabolic systems
Irena Lasiecka, Roberto Triggiani
出版情報: Cambridge ; New York : Cambridge University Press, 2000  xxi, 644 p.
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 74 . Control theory for partial differential equations : continuous and approximation theories / Irena Lasiecka, Roberto Triggiani ; v. 1
所蔵情報: loading…
3.

図書
図書
3. Abstract hyperbolic-like systems over a finite time horizon
Irena Lasiecka, Roberto Triggiani
出版情報: Cambridge ; New York : Cambridge University Press, 2000  xxi, 645-1067 p.
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 75 . Control theory for partial differential equations : continuous and approximation theories / Irena Lasiecka, Roberto Triggiani ; v. 2
所蔵情報: loading…
目次情報: 続きを見る
Categories / 1：
Categories and exact sequences / 2：
Change of rings / 3：
The Morita theory / 4：
Limits in categories / 5：
Localization / 6：
Local-global methods / 7：
Categories / 1：
Categories and exact sequences / 2：
Change of rings / 3：
4.

図書
図書
4. Tools for PDE : pseudodifferential operators, paradifferential operators, and layer potentials
Michael E. Taylor
出版情報: Providence, R.I. : American Mathematical Society, c2000  x, 257 p. ; 27 cm
シリーズ名: Mathematical surveys and monographs ; v. 81
所蔵情報: loading…
5.

図書
図書
5. Partial differential equations
Jürgen Jost
出版情報: New York ; Tokyo : Springer, c2002  xi, 325 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 214
所蔵情報: loading…
目次情報: 続きを見る
Introduction
The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order
The maximum principle
Existence techniques
methods based on the maximum principle / I：
Parabolic methods / II：
The Head equation
The wave equation and its connections with the Laplace and heat equation
The heat equation, semigroups, and Brownian motion
The Dirichlet principle
Variational methods for the solution of PDE (Existence techniques III)
Sobolev spaces and L2 regularity theory
Strong solutions
The regularity theory of Schauder and the continuity method (Existence techniques IV)
The Moser iteration method and the reqularity theorem of de Giorgi and Nash
Banach and Hilbert spaces
The Lp-spaces
Bibliography
Introduction
The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order
The maximum principle
6.

図書
図書
6. Monotone flows and rapid convergence for nonlinear partial differential equations
V. Lakshmikantham and S. Köksal
出版情報: London : Taylor & Francis, c2003  x, 318 p. ; 26 cm
シリーズ名: Series in mathematical analysis and applications / Edited by Ravi P. Agarwal and Donal O'Regan ; v. 7
所蔵情報: loading…
7.

図書
図書
7. Trends in nonlinear analysis
Markus Kirkilionis ... [et al.] (eds.)
出版情報: Berlin ; Tokyo : Springer, c2003  xv, 419 p. ; 24 cm
所蔵情報: loading…
8.

図書
図書
8. Higher order partial differential equations in Clifford analysis : effective solutions to problems
Elena Obolashvili
出版情報: Boston : Birkhäuser, c2003  viii, 178 p. ; 24 cm
シリーズ名: Progress in mathematical physics / editors-in-chief Anne Boutet de Monvel, Gerald Kaiser ; v. 28
所蔵情報: loading…
9.

図書
図書
9. Stability estimates for hybrid coupled domain decomposition methods
Olaf Steinbach
出版情報: Berlin ; Tokyo : Springer, c2003  vi, 120 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1809
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Preliminaries / 1：
Sobolev Spaces / 1.1：
Saddle Point Problems / 1.2：
Finite Element Spaces / 1.3：
Projection Operators / 1.4：
Quasi Interpolation Operators / 1.5：
Stability Results / 2：
Piecewise Linear Elements / 2.1：
Dual Finite Element Spaces / 2.2：
Higher Order Finite Element Spaces / 2.3：
Biorthogonal Basis Functions / 2.4：
The Dirichlet-Neumann Map for Elliptic Boundary Value Problems / 3：
The Steklov-Poincaré Operator / 3.1：
The Newton potential / 3.2：
Approximation by Finite Element Methods / 3.3：
Approximation by Boundary Element Methods / 3.4：
Mixed Discretization Schemes / 4：
Variational Methods with Approximate Steklov-Poincaré Operators / 4.1：
Lagrange Multiplier Methods / 4.2：
Hybrid Coupled Domain Decomposition Methods / 5：
Dirichlet Domain Decomposition Methods / 5.1：
A Two-Level Method / 5.2：
Three-Field Methods / 5.3：
Neumann Domain Decomposition Methods / 5.4：
Numerical Results / 5.5：
Concluding Remarks / 5.6：
References
Introduction
Preliminaries / 1：
Sobolev Spaces / 1.1：
10.

図書
図書
10. Fourier analysis and partial differential equations
Rafael José Iorio, Jr., Valéria de Magalhães Iorio
出版情報: Cambridge : Cambridge University Press, 2001  xi, 411 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 70
所蔵情報: loading…
目次情報: 続きを見る
Fourier Series and Periodic Distributions / Part I：
Preliminaries / 1：
Fourier series: basic theory / 2：
Periodic distributions and Sobolev spaces / 3：
Applications to Partial Differential Equations / Part II：
Linear equations / 4：
Nonlinear evolution equations / 5：
The Korteweg-de Vries / 6：
Distributions, Fourier transforms and linear equations / Part III：
KdV, BO and friends / 8：
Tools from the theory of ODEs / Appendix A：
Commutator estimates / Appendix B：
Bibliography
Index
Fourier Series and Periodic Distributions / Part I：
Preliminaries / 1：
Fourier series: basic theory / 2：
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼