Bilinear Estimates in the Presence of a Large Potential and a Critical NLS in 3D
Author: Fabio Pusateri
Publisher: American Mathematical Society
Published: 2024-08-19
Total Pages: 120
ISBN-13: 1470470675
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Bilinear Estimates in the Presence of a Large Potential and a Critical NLS in 3D
Author: Fabio Pusateri
Publisher:
Published: 2024
Total Pages: 0
ISBN-13: 9781470470678
DOWNLOAD EBOOKWe propose an approach to nonlinear evolution equations with large and decaying external potentials that addresses the question of controlling globally-in-time the nonlinear interactions of localized waves in this setting. This problem arises when studying localized perturbations around (possibly non-decaying) special solutions of evolution PDEs, and trying to control the projection onto the continuous spectrum of the nonlinear radiative interactions.
Implementing Spectral Methods for Partial Differential Equations
Author: David A. Kopriva
Publisher: Springer Science & Business Media
Published: 2009-05-27
Total Pages: 397
ISBN-13: 9048122619
DOWNLOAD EBOOKThis book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.
Introduction to Nonlinear Dispersive Equations
Author: Felipe Linares
Publisher: Springer
Published: 2014-12-15
Total Pages: 308
ISBN-13: 1493921819
DOWNLOAD EBOOKThis textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.
Advanced Calculus (Revised Edition)
Author: Lynn Harold Loomis
Publisher: World Scientific Publishing Company
Published: 2014-02-26
Total Pages: 595
ISBN-13: 9814583952
DOWNLOAD EBOOKAn authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Numerical Algorithms
Author: Justin Solomon
Publisher: CRC Press
Published: 2015-06-24
Total Pages: 400
ISBN-13: 1482251892
DOWNLOAD EBOOKNumerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Global Solutions of Nonlinear Schrodinger Equations
Author: Jean Bourgain
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 193
ISBN-13: 0821819194
DOWNLOAD EBOOKThis volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with Large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented and several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs.
Lectures on Modern Convex Optimization
Author: Aharon Ben-Tal
Publisher: SIAM
Published: 2001-01-01
Total Pages: 500
ISBN-13: 0898714915
DOWNLOAD EBOOKHere is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
Semilinear Schrodinger Equations
Author: Thierry Cazenave
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 346
ISBN-13: 0821833995
DOWNLOAD EBOOKThe nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.
Compactness and Contradiction
Author: Terence Tao
Publisher: American Mathematical Soc.
Published: 2013-03-22
Total Pages: 271
ISBN-13: 0821894927
DOWNLOAD EBOOKThere are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and nonrigorous to be discussed in the formal literature. Traditionally, it was a matter
