Wazwaz, A.- M.
Partial Differential Equations and Solitary Waves Theory
Springer-Verlag 2009.9
700 pp.(H)
ISBN 3-642-00250-1
29,800円
Contents
1. Basic Concepts/ 2. First Order PDE/ 3. One-Dimensional Heat Flow/ 4. Higher Dimensional Heat Flow/ 5. One Dimensional Wave Equation/ 6. Higher Dimensional Wave Equation/ 7. Laplace's Equation/ 8. Nonlinear Equations/ 9. Physical Models/ 10. Numerical Applications/ 11. Solitons and Compactons/ 12. Solitary Wave Theory/ 13. The Family of the KdV Equations/ 14. KdV and mKdV Equations of Higher-Orders/ 15. Family of KdV-Type Equations/ 16. Boussinesq, Klein-Gordon and Liouville Equations/ 17. Burgers, Fisher and Related Equations/ 18. Camassa-Holm and Schrodinger Equations/ Index/ *
Holden, H. et al.
Stochastic Partial Differential Equations 2nd ed.
A Modeling, White Noise Functional Approach
（確率偏微分方程式 第２版）
Springer-Verlag 2009.12
305 pp.(P)
ISBN 0-387-89487-X
10,100円
Contents
1. Introduction/ 2. Framework/ 3. Applications to Stochastic Ordinary Differential Equations/ 4. Stochastic Partial Differential Equations Driven by Brownian White Noise/ 5. Stochastic Partial Differential Equations Driven by Levy Processes/ Appendix A - E/ References/ List of frequently used notation and symbols/ Index/
* The first part of the book deals with the classical Brownian motion case. The second extends it to the Lﾃｩvy white noise case. For SPDEs of the Wick type, a general solution method is given by means of the Hermite transform, which turns a given SPDE into a parameterized family of deterministic PDEs. Applications of this theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. *
Alinhac, S.
Hyperbolic Partial Differential Equations
Springer-Verlag 2009.6
150 pp.(P)
ISBN 0-387-87822-X
8,800円
Contents
1. Vector Fields and Integral Curves/ 2. Operators and Systems in the Plane/ 3. Nonlinear First Order Equations/ 4. Conservation Laws in One-Space Dimension/ 5. The Wave Equation/ 6. Energy Inequalities for the Wave Equation/ 7. Variable Coefficient Wave Equations and Systems/ Appendix/ References/ Index/
* Serge Alinhac (1948―) received his PhD from l'Universite Paris-Sud XI (Orsay). After teaching at l'Universite Paris Diderot VII and Purdue University, he has been a professor of mathematics at l'Universite Paris-Sud XI (Orsay) since 1978. He is the author of Blowup for Nonlinear Hyperbolic Equations (Birkhar､user, 1995) and Pseudo-differential Operators and the Nash―Moser Theorem (with P. Gerard, American Mathematical Society, 2007). His primary areas of research are linear and nonlinear partial differential equations. *
Powers, D.
Boundary Value Problems 6th ed.
and Partial Differential Equations
（境界値問題と偏微分方程式 第６版）
Academic Press 2009.7
520 pp.(H)
ISBN 0-12-374719-8
10,800円
Contents
1. Differential Equations/ 2. Fourier Series and Integrals/ 3. The Heat Equation/ 4. The Wave Equation/ 5. The Potential Equation/ 6. Higher Dimensions & Other Coordinates/ 7. Laplace Transform/ 8. Numerical Methods/ Bibliography/ Appendix/ Answers to Odd Numbered Exercises/ Index/ *
Barbu, V.
Nonlinear Differential Equations of Monotone Types in Banach Spaces
Springer-Verlag 2010.1
272 pp.(H)
ISBN 1-4419-5541-0
12,800円
Contents
1. Fundamental Functional Analysis/ 2. Maximal Monotone Operators in Banach Spaces/ 3. Accretive Nonlinear Operators in Banach Spaces/ 4. The Cauchy Problem in Banach Spaces/ 5. Existence Theory of Nonlinear Dissipative Dynamics/ Index/
* This book is concerned with basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. *
Troltzsch, F.
Optimal Control of Partial Differential Equations Vol.112
Theory, Methods and Applications
AMS 2010.4
399 pp.(H)
ISBN 0-8218-4904-2
8,900円
Contents
1. Introduction and examples/ 2. Linear-quadratic elliptic control problems/ 3. Linear-quadratic parabolic control problems/ 4. Optimal control of semilinear elliptic equations/ 5. Optimal control of semilinear parabolic equations/ 6. Optimization problems in Banach spaces/ 7. Supplementary results on partial differential equations/ Bibliography/ Index/
* Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines.
* This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. *
Pivato, M.
Linear Partial Differential Equations and Fourier Theory
Cambridge University Press 2010.2
630 pp.(P)
ISBN 0-521-13659-8
7,700円
Contents
1. Motivating Examples and Major Applications/ 2. General Theory/ 3. Fourier Series on Bounded Domains/ 4. BVP Solutions Via Eigenfunction Expansions/ 5. Miscellaneous Solution Methods/ 6. Fourier Transforms on Unbounded Domains/ Appendices/ References/ Index/ *
Cifuentes, P. et al. ed.
Harmonic Analysis and Partial Differential Equations
AMS 2010.2
249 pp.(P)
ISBN 0-8218-4770-8
10,200円
Contents
1. Instance optimal decoding by thresholding in compressed sensing/ 2. Local $T(b)$ theorems and applications in PDE/ 3. The global behavier of solutions to critical nonlinear dispersive and wave equations/ 4. Weighted norm inequalities, off-diagonal estimates and elliptic operators/ 5. Heat-flow monotonicity related to some inequalities in euclidean analysis/ 6. A uniform sublevel set estimate/ 7. On a quadratic estimate related to the Kato conjecture and boundary value problems/ 8. Flag paraproducts/ 9. The Polya-Tchebotarov problem/ 10. Iterated Riesz commutators: a simple proof of boundedness/ 11. A mixed norm variant of Wolff's inequality for paraboloids/ 12. On the unreasonable effectiveness of Gutzmer's formula/ 13. Bilinear virial identities and oscillatory integrals/ 14. On the properties of the integer translates of a square integrable function/ Index/
* This volume contains the Proceedings of the 8th International Conference on Harmonic Analysis and Partial Differential Equations, held in El Escorial, Madrid, Spain, on June 16-20, 2008. *
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