Format: Hardback, 174 pages, height x width: 240x168 mm, weight: 502 g, 35 Tables,
color; 2 Illustrations, color; 1 Illustrations, black and white; XII, 174 p. 3 illus., 2 illus. in color.
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 29-Oct-2022
ISBN-13: 9783031170683
This textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, readers are introduced to techniques to obtain exact solutions of NLPDEs. The chapters include the following topics: Nonlinear PDEs are Everywhere; Differential Substitutions; Point and Contact Transformations; First Integrals; and Functional Separability. Readers are guided through these chapters and are provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. This Second Edition includes a new method of generating contact transformations and focuses on a solution method (parametric Legendre transformations) to solve a particular class of two nonlinear PDEs.
Nonlinear PDEs are Everywhere.- Differential Substitutions.- Point and Contact Transformations.- First Integrals.- Functional Separability.
Format: Hardback, 1160 pages, height x width: 235x155 mm,
94 Tables, color; VIII, 1160 p.,
Pub. Date: 25-Dec-2022
ISBN-13: 9783031191107
Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume ? compiled on the occasion of his 60th birthday ? are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Helmut Hofer, Alberto Abbondandolo, Urs Frauenfelder, Felix Schlenk, Dedication.- Peter Albers, Serge Tabachnikov, Symplectically convex and symplectically star-shaped curves: A variational problem.- Marcelo R. R. Alves, Lucas Dahinden, Matthias Meiwes, Louis Merlin, C^0-robustness of topological entropy for geodesic flows.- Luca Asselle, Marco Fenucci, Alessandro Portaluri, Bifurcations of balanced configurations for the Newtonian n-body problem in R^4.- Gabriele Benedetti, Jungskoo Kang, Relative Hofer-Zehnder capacity and positive symplectic homology.- Lev Buhovsky, Vincent Humiliere, Sobhan Seyfaddini, An Arnold-type prinicple for non-smooth objects.- Lev Buhovsky, Emmanuel Opshtein, Quantitative h-principle in symplectic geometry.- Franco Cardin, On symplectomorphisms and Hamiltonian Flows.- Roger Casals, Lagrangian skeleta and plane curve singularities.- Baptiste Chantraine, Reeb chords of Lagrangian Slices.- Marc Chaperon, Basic facts and naive questions.- Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel, Another look at the Hofer-Zehnder conjecture.- Daniel Cristofaro-Gardiner, Richard Hind, Kyler Siegel, Higher symplectic capacities and the stabilized embedding problem for integral elllipsoids.- Guido de Philippis, Michele Marini, Marco Mazzucchelli, Stefan Suhr, Closed geodesics on reversible Finsler 2-spheres.- Michael Entov, Leonid Polterovich, Legendrian persistance modules and dynamics.- Jonathan David Evans, A Lagrangian Klein bottle you can't squeeze.- Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono, Construction of a linear K-system in Hamiltonian Floer theory.- Hansjoerg Geiges, What does a vector field know about volume?- Paolo Ghiggini, Klaus Niederkruger-Eid, On the symplectic fillings of standard real projective spaces.- Alexey Glutsyuk, On curves with the Poritsky property.- Jean Gutt, Michael Hutchings, Vinicius G. B. Ramos, Examples around the strong Viterbo conjecture.- Umberto L. Hryniewicz, Pedro A. S. Salomao, Richard Siefring, Global surfaces of section with positive genus for dynamically convex Reeb flows.- Michael Hutchings, ECH capacities and the Ruelle invariant.- Kei Ire, Capacities of billiard tables and S^1-equivariant loop space homology.- Joontae Kim, Seongchan Kim, Myeonggi Kwon, Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities.- Myeonggi Kwon, Kevin Wiegand, Kai Zehmisch, Diffeomorphism type via aperiodicity in Reeb dynamics.- Patrice Le Calvez, Conservative surface homeomorphisms with finitely many periodic points.- Frederic Le Roux, Sobhan Seyfaddini, The Anosov-Katok method and pseudo-rotations in symplectic dynamics.- Agustin Moreno, Contact geometry in the restricted three-body problem: a survey.- Agustin Moreno, Otto van Koert, A generalized Poincare-Birkhoff theorem.- Georgios Dimitroglou Rizell, Families of Legendrians and Lagrangians with unbounded spectral norm.- Paul Seidel, Nicholas Wilkins, Covariant constancy of quantum Steenrod operations.- Vivek Shende, An algebraic approach to the algebraic Weinstein conjecture.- Matthew Strom Borman, Nick Sheridan, Umut Varolgunes, Quantum cohomology as a deformation of symplectic cohomology.- Fabian Ziltener, A symplectic embedding of the cube with minimal sections and a question by Schlenk.
Format: Hardback, 210 pages, height x width: 235x155 mm, 5 Illustrations, color;
1 Illustrations, black and white; X, 210 p. 6 illus., 5 illus. in color
Series: Springer INdAM Series 52
Pub. Date: 08-Dec-2022
ISBN-13: 9789811964336
This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schroedinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature.
Part I: Long-time behavior of NLS-type equations.- 1 Scipio Cuccagna, Note on small data soliton selection for nonlinear Schroedinger equations with potential.- 2 Jacopo Bellazzini and Luigi Forcella, Dynamics of solutions to the Gross-Pitaevskii equation describing dipolar Bose-Einstein condensates.- Part II: Probabilistic and nonstandard methods in the study of NLS equations.- 3 Renato Luca, Almost sure pointwise convergence of the cubic nonlinear Schroedinger equation on T^2.- 4 Nevena Dugandzija and Ivana Vojnovic, Nonlinear Schroedinger equation with singularities.- Part III: Dispersive properties.- 5 Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone, Schroedinger flow's dispersive estimates in a regime of re-scaled potentials.- 6 Federico Cacciafesta, Eric Sere, Junyong Zhang, Dispersive estimates for the Dirac-Coulomb equation.- 7 Matteo Gallone, Alessandro Michelangeli, Eugenio Pozzoli, Heat equation with inverse-square potential of bridging type across two half-lines.- Part IV: Wave and Kdv-type equations.- 8 Felice Iandoli, On the Cauchy problem for quasi-linear Hamiltonian KdV-type equations.- 9 Vladimir Georgiev and Sandra Lucente, Linear and nonlinear interaction for wave equations with time variable coefficients.- 10 Matteo Gallone and Antonio Ponno, Hamiltonian field theory close to the wave equation: from Fermi-Pasta-Ulam to water waves.
Format: Hardback, 487 pages, height x width: 235x155 mm, 14 Tables, color; 15 Illustrations, color;
6 Illustrations, black and white; XIX, 487 p. 21 illus., 15 illus. in color
Series: Progress in Nonlinear Differential Equations and Their Applications 101
Pub. Date: 02-Jan-2023
ISBN-13: 9783031174940
This monograph considers the analytical and geometrical questions emerging from the study of thin elastic films that exhibit residual stress at free equilibria. It provides the comprehensive account, the details and background on the most recent results in the combined research perspective on the classical themes: in Differential Geometry ? that of isometrically embedding a shape with a given metric in an ambient space of possibly different dimension, and in Calculus of Variations ? that of minimizing non-convex energy functionals parametrized by a quantity in whose limit the functionals become degenerate.
Prestressed thin films are present in many contexts and applications, such as: growing tissues, plastically strained sheets, engineered swelling or shrinking gels, petals and leaves of flowers, or atomically thin graphene layers. While the related questions about the physical basis for shape formation lie at the intersection of biology, chemistry and physics, fundamentally they are of the analytical and geometrical character, and can be tackled using the techniques of the dimension reduction, laid out in this book.
The text will appeal to mathematicians and graduate students working in the fields of Analysis, Calculus of Variations, Partial Differential Equations, and Applied Math. It will also be of interest to researchers and graduate students in Engineering (especially fields related to Solid Mechanics and Materials Science), who would like to gain the modern mathematical insight and learn the necessary tools.
Introduction.- Part I: Tools in Mathematical Analysis.- -Convergence.- Korn's Inequality.- Friesecke-James-Muller's Inequality.- Part II: Dimension Reduction in Classical Elasticity.- Limiting Theories for Elastic Plates and Shells: Nonlinear Bending.- Limiting Theories for Elastic Plates and Shells: Sublinear and Linear.- Linear Theories for Elastic Plates: Linearized Bending.- Infinite Hierarchy of Elastic Shell Models.- Limiting Theories on Elastic Elliptic Shells.- Limiting Theories on Elastic Developable Shells.- Part III: Dimension Reduction in Prestressed Elasticity.- Limiting Theories for Prestressed Films: Nonlinear Bending.- Limiting Theories for Prestressed Films: Von Karman-like Theory.- Infinite Hierarchy of Limiting Theories for Prestressed Films.- Limiting Theories for Weakly Prestressed Films.- Terminology and Notation.- Index.
Format: Hardback, 170 pages, height x width: 240x168 mm, V, 170 p
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 14-Jan-2023
ISBN-13: 9783031220869
Author Biography
Goodreads reviews
This textbook is an introduction to the methods needed to solve partial differential equations (PDEs). Readers are introduced to PDEs that come from a variety of fields in engineering and the natural sciences. The chapters include the following topics: First Order PDEs, Second Order PDEs, Fourier Series, Separation of Variables, and the Fourier Transform and higher dimensional problems. Readers are guided through these chapters where techniques for solving first and second order PDEs are introduced. Each chapter ends with series of exercises to facilitate learning as well as illustrate the material presented in each chapter.
Introduction.- First Order PDEs.- Second Order Linear PDEs.- Fourier Series.- Separation of Variables.- Fourier Transform.
Format: Hardback, 536 pages, height x width: 235x155 mm, 13 Illustrations,
black and white; XII, 536 p. 13 illus.,
Pub. Date: 08-Jan-2023
ISBN-13: 9783031158308
Welington de Melo (Guape, 1946 - Rio de Janeiro, 2016) was a brazilian mathematician whose contributions were deeply connected with Smale and Palis school of dynamical systems. In particular the classification of smooth dynamical systems and the study of its generic properties are recurrent topics in his work. This book collected some of his most significant contributions, from his early work on structural stability of diffeomorphisms in the 1970's to his groundbreaking results on one-dimensional dynamics. Indeed his interest in one-dimensional dynamics is a clear distinction from early influences. An effervescent work in discrete dynamics on the interval and the circle started in the 1970s. It was soon realized that those systems have surprisingly rich dynamics. But, at the same time, an impressive set of tools were developed to study them. There are two main sets of tools. Real methods such as bounded distortion control via Schwarzian derivative and later cross-ratio estimates allows one to understand some of its features. However, often complex methods, with deep connections with Teichmuller theory, are necessary to obtain some of the most striking results. This is especially true in renormalization theory, a theme Welington was very fond of, and that appears prominently in his collected works. Welington played an important role in the development on both fronts, and this book is a testament of his influence in the field which resonates to this day.