On Stability Of Type Ii Blow Up For The Critical Nonlinear Wave Equation In Mathbb R 3 1
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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.
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.
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.
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.
Anomalies In Partial Differential Equations
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Author : Massimo Cicognani
language : en
Publisher: Springer Nature
Release Date : 2021-02-03
Anomalies In Partial Differential Equations written by Massimo Cicognani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-03 with Mathematics categories.
The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza". The volume contains results for well-posedness and local solvability for linear models with low regular coefficients. Moreover, nonlinear dispersive models (damped waves, p-evolution models) are discussed from the point of view of critical exponents, blow-up phenomena or decay estimates for Sobolev solutions. Some contributions are devoted to models from applications as traffic flows, Einstein-Euler systems or stochastic PDEs as well. Finally, several contributions from Harmonic and Time-Frequency Analysis, in which the authors are interested in the action of localizing operators or the description of wave front sets, complete the volume.
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.
Elliptic Partial Differential Equations
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Author : Lucio Boccardo
language : en
Publisher: Walter de Gruyter
Release Date : 2013-10-29
Elliptic Partial Differential Equations written by Lucio Boccardo and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-29 with Mathematics categories.
Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
Ordinary Differential Equations With Applications
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Author : Carmen Chicone
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-08
Ordinary Differential Equations With Applications written by Carmen Chicone 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 2008-04-08 with Mathematics categories.
This book is based on a two-semester course in ordinary di?erential eq- tions that I have taught to graduate students for two decades at the U- versity of Missouri. The scope of the narrative evolved over time from an embryonic collection of supplementary notes, through many classroom tested revisions, to a treatment of the subject that is suitable for a year (or more) of graduate study. If it is true that students of di?erential equations giveaway their point of viewbythewaytheydenotethederivativewith respecttotheindependent variable, then the initiated reader can turn to Chapter 1, note that I write x ?,not x , and thus correctly deduce that this book is written with an eye toward dynamical systems. Indeed, this book contains a thorough int- duction to the basic properties of di?erential equations that are needed to approach the modern theory of (nonlinear) dynamical systems. However, this is not the whole story. The book is also a product of my desire to demonstrate to my students that di?erential equations is the least insular of mathematical subjects, that it is strongly connected to almost all areas of mathematics, and it is an essential element of applied mathematics.
Semilinear Schrodinger Equations
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Author : Thierry Cazenave
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Semilinear Schrodinger Equations written by Thierry Cazenave 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 2003 with Mathematics categories.
The 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.