Type Ii Blow Up Solutions With Optimal Stability Properties For The Critical Focussing Nonlinear Wave Equation On Mathbb R 3 1
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Type Ii Blow Up Solutions With Optimal Stability Properties For The Critical Focussing Nonlinear Wave Equation On Mathbb R 3 1
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Author : Stefano Burzio
language : en
Publisher: American Mathematical Society
Release Date : 2022-07-18
Type Ii Blow Up Solutions With Optimal Stability Properties For The Critical Focussing Nonlinear Wave Equation On Mathbb R 3 1 written by Stefano Burzio and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-18 with Mathematics categories.
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Mathematics Of Wave Phenomena
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Author : Willy Dörfler
language : en
Publisher: Springer Nature
Release Date : 2020-10-01
Mathematics Of Wave Phenomena written by Willy Dörfler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-01 with Mathematics categories.
Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.
Nonlinear Optics In Telecommunications
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Author : Thomas Schneider
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-15
Nonlinear Optics In Telecommunications written by Thomas Schneider and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-15 with Science categories.
This comprehensive and didactic overview explores the nonlinear effects from a physical point of view and discusses the implications for signal capacity. Enriched with practical considerations and experimental results, the book offers special chapters dealing with applications of nonlinear effects for signal processing, ultrafast-optical switching, wavelength conversion, nonlinear amplification, and optical phase-conjugation. Equipped with chapter-end summaries and problems, this valuable reference can also serve as a graduate-level textbook.
Linear And Quasi Linear Equations Of Parabolic Type
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Author : Olʹga Aleksandrovna Ladyzhenskai͡a
language : en
Publisher: American Mathematical Soc.
Release Date : 1968
Linear And Quasi Linear Equations Of Parabolic Type written by Olʹga Aleksandrovna Ladyzhenskai͡a and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Fourier Analysis And Nonlinear Partial Differential Equations
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Author : Hajer Bahouri
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-03
Fourier Analysis And Nonlinear Partial Differential Equations written by Hajer Bahouri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-03 with Mathematics categories.
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
Beyond Perturbation
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Author : Shijun Liao
language : en
Publisher: CRC Press
Release Date : 2003-10-27
Beyond Perturbation written by Shijun Liao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-27 with Mathematics categories.
Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for
On Stability Of Type Ii Blow Up For The Critical Nonlinear Wave Equation In Mathbb R 3 1
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Author : Joachim K Krieger
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
On Stability Of Type Ii Blow Up For The Critical Nonlinear Wave Equation In Mathbb R 3 1 written by Joachim K Krieger and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
The author shows that the finite time type II blow up solutions for the energy critical nonlinear wave equation $ Box u = -u^5 $ on $mathbb R^3+1$ constructed in Krieger, Schlag, and Tataru (2009) and Krieger and Schlag (2014) are stable along a co-dimension three manifold of radial data perturbations in a suitable topology, provided the scaling parameter $lambda (t) = t^-1-nu $ is sufficiently close to the self-similar rate, i. e. $nu >0$ is sufficiently small. Our method is based on Fourier techniques adapted to time dependent wave operators of the form $ -partial _t^2 + partial _r^2 + frac 2rpartial _r +V(lambda (t)r) $ for suitable monotone scaling parameters $lambda (t)$ and potentials $V(r)$ with a resonance at zero.
Variational Topological And Partial Order Methods With Their Applications
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Author : Zhitao Zhang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-17
Variational Topological And Partial Order Methods With Their Applications written by Zhitao Zhang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-17 with Mathematics categories.
Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.
Fourier Series In Control Theory
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Author : Vilmos Komornik
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-01-27
Fourier Series In Control Theory written by Vilmos Komornik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-27 with Computers categories.
This book is the first serious attempt to gather all of the available theory of "nonharmonic Fourier series" in one place, combining published results with new results by the authors.
Hidden Dynamics
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Author : Mike R. Jeffrey
language : en
Publisher: Springer
Release Date : 2018-12-11
Hidden Dynamics written by Mike R. Jeffrey and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-11 with Mathematics categories.
The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical properties. From biological mitosis to seizures. From rattling machine parts to earthquakes. From individual decisions to economic crashes. Where discontinuities occur, determinacy is inevitably lost. Typically the physical laws of such change are poorly understood, and too ill-defined for standard mathematics. Discontinuities offer a way to make the bounds of scientific knowledge a part of the model, to analyse a system with detail and rigour, yet still leave room for uncertainty. This is done without recourse to stochastic modeling, instead retaining determinacy as far as possible, and focussing on the geometry of the many outcomes that become possible when it breaks down. In this book the foundations of `piecewise-smooth dynamics' theory are rejuvenated, given new life through the lens of modern nonlinear dynamics and asymptotics. Numerous examples and exercises lead the reader through from basic to advanced analytical methods, particularly new tools for studying stability and bifurcations. The book is aimed at scientists and engineers from any background with a basic grounding in calculus and linear algebra. It seeks to provide an invaluable resource for modeling discontinuous systems, but also to empower the reader to develop their own novel models and discover as yet unknown phenomena.