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1. Nonlinear PDEs : Mathematical Models in Biology, Chemistry and Population Genetics
by Marius Ghergu, Vicenţiu D. Rӑdulescu
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2012
シリーズ名: Springer Monographs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-3-642-22664-9
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2. Linear Integral Equations : Theory & Technique
by Ram P. Kanwal
出版情報: New York, NY : Springer New York : Imprint: Birkhäuser, 2013
シリーズ名: Modern Birkhäuser Classics ;
オンライン: http://dx.doi.org/10.1007/978-1-4614-6012-1
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Introduction
Integral Equations with Separable Kernels
Method Of Successive Approximations
Classical Fredholm Theory.- Applications of Ordinary Differential Equations.- Applications of Partial Differential Equations
Symmetric Kernels
Singular Integral Equations
Integral Transformation Methods
Applications to Mixed Boundary Value Problems
Integral Equations Perturbation Methods
Appendix
Bibliography
Index
Introduction
Integral Equations with Separable Kernels
Method Of Successive Approximations
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3. The Kolmogorov-Obukhov Theory of Turbulence : A Mathematical Theory of Turbulence
by Bjorn Birnir
出版情報: New York, NY : Springer New York : Imprint: Springer, 2013
シリーズ名: SpringerBriefs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-1-4614-6262-0
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1.The Mathematical Formulation of Fully-Developed Turbulence
2.Probability and the Statistical Theory of Turbulence
3.The Invariant Measure and the Probability Density Function
4. Existence Theory of Swirling Flow
The Bound for a Swirling Flow
Detailed estimates of S2 and S3
The Generalized Hyperbolic Distributions
References
1.The Mathematical Formulation of Fully-Developed Turbulence
2.Probability and the Statistical Theory of Turbulence
3.The Invariant Measure and the Probability Density Function
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4. Progress in Partial Differential Equations : Asymptotic Profiles, Regularity and Well-Posedness
edited by Michael Reissig, Michael Ruzhansky
出版情報: Heidelberg : Springer International Publishing : Imprint: Springer, 2013
シリーズ名: Springer Proceedings in Mathematics & Statistics ; 44
オンライン: http://dx.doi.org/10.1007/978-3-319-00125-8
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Preface
Global Existence and Energy Decay of Solutions for a Nondissipative Wave Equation with a Time-Varying Delay Term
Non-uniqueness and uniqueness in the Cauchy problem of elliptic and backward-parabolic equations
On internal regularity of solutions to the initial value problem for the Zakharov–Kuznetsov equation
Singular semilinear elliptic equations with subquadratic gradient terms
On the parabolic regime of a hyperbolic equation with weak dissipation: the coercive case
H¥ well-posedness for degenerate p-evolution models of higher order with time-dependent coefficients
On the global solvability for semilinear wave equations with smooth time dependent propagation speeds
Filippov Solutions to Systems of Ordinary Differential Equations with Delta Function Terms as Summands
Resolvent estimates and scattering problems for Schr¨odinger, Klein-Gordon and wave equations
On an Optimal Control Problem for the Wave Equation in One Space Dimension Controlled by Third Type Boundary Data
Critical exponent for the semilinear wave equation with time or space dependent damping
A note on a class of conservative, well-posed linear control systems
Recent progress in smoothing estimates for evolution equations
Differentiability of Inverse Operators
Quasi-symmetrizer and hyperbolic equations
Solution of the Cauchy problem for generalized Euler-Poisson-Darboux equation by the method of fractional integrals
Global Solutions of Semilinear System of Klein-Gordon Equations in de Sitter Spacetime
Preface
Global Existence and Energy Decay of Solutions for a Nondissipative Wave Equation with a Time-Varying Delay Term
Non-uniqueness and uniqueness in the Cauchy problem of elliptic and backward-parabolic equations
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5. The Mimetic Finite Difference Method for Elliptic Problems
by Lourenço Beirão Veiga, Konstantin Lipnikov, Gianmarco Manzini
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: MS&A - Modeling, Simulation and Applications ; 11
オンライン: http://dx.doi.org/10.1007/978-3-319-02663-3
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1 Model elliptic problems
2 Foundations of mimetic finite difference method
3 Mimetic inner products and reconstruction operators
4 Mimetic discretization of bilinear forms
5 The diffusion problem in mixed form
6 The diffusion problem in primal form
7 Maxwells equations. 8. The Stokes problem. 9 Elasticity and plates
10 Other linear and nonlinear mimetic schemes
11 Analysis of parameters and maximum principles
12 Diffusion problem on generalized polyhedral meshes
1 Model elliptic problems
2 Foundations of mimetic finite difference method
3 Mimetic inner products and reconstruction operators
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6. Multiscale Modeling of Pedestrian Dynamics
by Emiliano Cristiani, Benedetto Piccoli, Andrea Tosin
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: MS&A, Modeling, Simulation and Applications ; 12
オンライン: http://dx.doi.org/10.1007/978-3-319-06620-2
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1 An Introduction to the Modeling of Crowd Dynamics
2 Problems and Simulations
3 Psychological Insights
4 An Overview of the Modeling of Crowd Dynamics
5 Multiscale Modeling by Time-Evolving Measures
6 Basic Theory of Measure-Based Models
7 Evolution in Measure Spaces with Wasserstein Distance
8 Generalizations of the Multiscale Approach
9 Appendices: A Basics of Measure and Probability Theory; B Pseudo-Code for the Multiscale Algorithm
1 An Introduction to the Modeling of Crowd Dynamics
2 Problems and Simulations
3 Psychological Insights
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7. Analytic Methods in Interdisciplinary Applications
edited by Vladimir V. Mityushev, Michael Ruzhansky
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Springer Proceedings in Mathematics & Statistics ; 116
オンライン: http://dx.doi.org/10.1007/978-3-319-12148-2
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Omer H. Abdelrahman, Erol Gelenbe: Search in Big Networks and Big Data
David Applebaum, Rodrigo Banuelos: Probabilistic Approach to Fractional Integrals and the Hardy‐Littlewood‐Sobolev Inequality
R. V. Craster: Dynamic homogenization
Tadeusz Czachorski: Queueing Models for Performance Evaluation of Computer Networks ‐Transient State Analysis
Tokio Matsuyama, Michael Ruzhansky: Global well‐posedness of the Kirchhoff equation and Kirchhoff systems
Wieslaw L. Nowinski: Brain atlasing: design principles, methods, tools and applications
Grigory Panasenko: Method of asymptotic partial domain decomposition for nonsteady problems: wave equation on a thin structure
Aleksandr Rusakov: The first student of Andrei Nikolaevich Kolmogorov
M. Zhuravkov, L.Drozd, N. Romanova, A. Krupoderov: Mechanical-mathematical modelling of biological tissue behavior
Omer H. Abdelrahman, Erol Gelenbe: Search in Big Networks and Big Data
David Applebaum, Rodrigo Banuelos: Probabilistic Approach to Fractional Integrals and the Hardy‐Littlewood‐Sobolev Inequality
R. V. Craster: Dynamic homogenization
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8. Partial Differential Equations in Action : Complements and Exercises
by Sandro Salsa, Gianmaria Verzini
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: UNITEXT ; 87
オンライン: http://dx.doi.org/10.1007/978-3-319-15416-9
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1 Diffusion
2 The Laplace equation
3 First order equations
4 Waves
5 Functional analysis
6 Variational formulations
7 Appendix A Sturm-Liouville, Legendre and Bessel equations
8 Appendix B Identities
1 Diffusion
2 The Laplace equation
3 First order equations
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9. Methods of Mathematical Modelling : Continuous Systems and Differential Equations. 1st ed. 2015
by Thomas Witelski, Mark Bowen
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Springer Undergraduate Mathematics Series ;
オンライン: http://dx.doi.org/10.1007/978-3-319-23042-9
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Rate equations
Transport equations
Variational principles
Dimensional scaling analysis
Self-similar scaling solutions of differential equations
Perturbation methods
Boundary layer theory
Long-wave asymptotics for PDE problems
Weakly-nonlinear oscillators
Fast/slow dynamical systems
Reduced models for PDE problems
Modelling in applied fluid dynamics
Rate equations
Transport equations
Variational principles
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10. Error Estimates for Well-Balanced Schemes on Simple Balance Laws : One-Dimensional Position-Dependent Models. 1st ed. 2015
by Debora Amadori, Laurent Gosse
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: SpringerBriefs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-3-319-24785-4
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1 Introduction
2 Local and global error estimates
3 Position-dependent scalar balance laws
4 Lyapunov functional for inertial approximations
5 Entropy dissipation and comparison with Lyapunov estimates
6 Conclusion and outlook
1 Introduction
2 Local and global error estimates
3 Position-dependent scalar balance laws