MATHEMATICAL METHODS IN PHYSICS DISTRIBUTIONS HILBERT SPACE OPERATORS AND VARIATIONAL METHODS PROGRESS IN MATHEMATICAL PHYSICS VOL 26

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Author : Philippe Blanchard
ISBN : 9781461200499
Genre : Mathematics
File Size : 56.65 MB
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Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Author : Claudia Bucur
ISBN : 9783319287393
Genre : Mathematics
File Size : 59.16 MB
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Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.

The aim of the Sino–Japan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan. The topics discussed in this proceedings include mean curvature flows, KAM theory, N-body problems, flows on Riemannian manifolds, hyperbolic systems, vortices, water waves, and reaction diffusion systems. Contents:A Spectral Theory of Linear Operators on Rigged Hilbert Spaces Under Certain Analyticity Conditions (H Chiba)Conditional Fredholm Determinant and Trace Formula for Hamiltonian Systems: A Survey (X-J Hu and P-H Wang)Initial Value Problem for Water Waves and Shallow Water and Long Wave Approximations (T Iguchi)On the Existence and Nonexistence of Maximizers Associated with Trudinger-Moser Type Inequalities in Unbounded Domains (M Ishiwata)Computer-Assisted Uniqueness Proof for Stokes' Wave of Extreme Form (K Kobayashi)From the Boltzmann H-Theorem to Perelman's W-Entropy Formula for the Ricci Flow (X-D Li)The Spreading of a New Species with Free Boundaries (X Liu and B Lou)Recent Progress on Observability for Stochastic Partial Differential Equations (Q Lü and Z-Q Yin)The Nonlinear “Hot Spots” Conjecture in Balls of S2 and H2 (Y Miyamoto)Mean-Field Models Describing Micro Phase Separation in the Two-Dimensional Case (B Niethammer and Y Oshita)Global Existence of Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems (P Qu and C-M Liu)Time Averaged Properties Along Unstable Periodic Orbits of the Kuramoto-Sivashinsky Equation (Y Saiki and M Yamada)Anomalous Enstrophy Dissipation via the Self-Similar Triple Collapse of the Euler-α Point Vortices (T Sakajo)Action Minimizing Periodic Solutions in the N-Body Problem (M Shibayama)Some Geometric Problems of Conformally Compact Einstein Manifolds (Y Shi)Mathematical Modelling and Analysis of Droplet Motion on Obstacles (K Svadlenka)Introduction to Varifold and Its Curvature Flow (Y Tonegawa)Weak KAM Theory in Time-Periodic Lagrangian Systems (K-Z Wang and J Yan)A Note on Resonant Interaction of Rossby Waves in Two-Dimensional Flow on a β Plane (M Yamada and T Yoneda)Lp-Solvability of Nonlocal Parabolic Equations with Spatial Dependent and Non-Smooth Kernels (X-C Zhang)A Convergence Theorem of Kähler-Ricci Flow (Z-L Zhang)KP Approximation to the 3-D Water Wave Equations with Surface Tension (M Ming, P Zhang and Z-F Zhang)Smooth Convergence of Kähler-Ricci Flow on a Fano Manifold (X-H Zhu) Readership: Researchers and professionals in differential equations. Keywords:Differential Equations;Geometry Analysis;Mean Curvature Flows;KAM Theory;N-Body Problems;Flows On Riemannian Manifolds;Hyperbolic Systems;Vortices;Water Waves;Reaction Diffusion Systems

Author : K. F. Riley
ISBN : 9781139450997
Genre : Science
File Size : 67.95 MB
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The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

Author : Marius Ghergu
ISBN : STANFORD:36105131662970
Genre : Mathematics
File Size : 44.14 MB
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This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. There are carefully analyzed logistic type equations with boundary blow-up solutions and generalized Lane-Emden-Fowler equations or Gierer-Meinhardt systems with singular nonlinearity in anisotropic media. These nonlinear problems appear as mathematical models in various branches of Physics, Mechanics, Genetics, Economics, Engineering, and they are also relevant in Quantum Physics and Differential Geometry. One of the main purposes of this volume is to deduce decay rates for general classes of solutions in terms of estimates of particular problems. Much of the material included in this volume is devoted to the asymptotic analysis of solutions and to the qualitative study of related bifurcation problems. Numerical approximations illustrate many abstract results of this volume. A systematic description of the most relevant singular phenomena described in these lecture notes includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear singular phenomena

Author : R.R. Bowker Company
ISBN : UOM:39015054035236
Genre : American literature
File Size : 45.52 MB
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