On Stability Of Type Ii Blow Up For The Critical Nonlinear Wave Equation In Mathbb R 3 1

On Stability Of Type Ii Blow Up For The Critical Nonlinear Wave Equation In Mathbb R 3 1 Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of On Stability Of Type Ii Blow Up For The Critical Nonlinear Wave Equation In Mathbb R 3 1 book. This book definitely worth reading, it is an incredibly well-written.

On Stability of Type II Blow Up for the Critical Nonlinear Wave Equation in $mathbb {R}^{3+1}$

Joachim K Krieger
On Stability of Type II Blow Up for the Critical Nonlinear Wave Equation in mathbb R 3 1 Book PDF

Author : Joachim K Krieger
Publisher : American Mathematical Society
Page : 129 pages
File Size : 41,9 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470442996

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On Stability of Type II Blow Up for the Critical Nonlinear Wave Equation in $mathbb {R}^{3+1}$ by Joachim K Krieger Pdf

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 $mathbb {R}^{3+1}$

Stefano Burzio,Joachim Krieger
Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on mathbb R 3 1 Book PDF

Author : Stefano Burzio,Joachim Krieger
Publisher : American Mathematical Society
Page : 88 pages
File Size : 55,9 Mb
Release : 2022-07-18
Category : Mathematics
ISBN : 9781470453466

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Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $mathbb {R}^{3+1}$ by Stefano Burzio,Joachim Krieger Pdf

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Mathematics of Wave Phenomena

Willy Dörfler,Marlis Hochbruck,Dirk Hundertmark,Wolfgang Reichel,Andreas Rieder,Roland Schnaubelt,Birgit Schörkhuber
Mathematics of Wave Phenomena Book PDF

Author : Willy Dörfler,Marlis Hochbruck,Dirk Hundertmark,Wolfgang Reichel,Andreas Rieder,Roland Schnaubelt,Birgit Schörkhuber
Publisher : Springer Nature
Page : 330 pages
File Size : 49,7 Mb
Release : 2020-10-01
Category : Mathematics
ISBN : 9783030471743

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Mathematics of Wave Phenomena by Willy Dörfler,Marlis Hochbruck,Dirk Hundertmark,Wolfgang Reichel,Andreas Rieder,Roland Schnaubelt,Birgit Schörkhuber Pdf

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 Wave Equations

Walter A. Strauss
Nonlinear Wave Equations Book PDF

Author : Walter A. Strauss
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 51,7 Mb
Release : 1990-01-12
Category : Mathematics
ISBN : 9780821807255

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Nonlinear Wave Equations by Walter A. Strauss Pdf

The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.

Lectures on the Energy Critical Nonlinear Wave Equation

Carlos E. Kenig
Lectures on the Energy Critical Nonlinear Wave Equation Book PDF

Author : Carlos E. Kenig
Publisher : Unknown
Page : 161 pages
File Size : 52,7 Mb
Release : 2015
Category : MATHEMATICS
ISBN : 1470422735

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Lectures on the Energy Critical Nonlinear Wave Equation by Carlos E. Kenig Pdf

This monograph deals with recent advances in the study of the long-time asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the "concentration-compactness/rigidity theorem method" introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the "global regularity and well-posedness" conjecture (defocusing case) and the "ground-state" conjecture (focusing case) in critical dispersive problems. The second part of the monograph describes the.

On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation

Charles Collot,Pierre Raphaël,Jeremie Szeftel
On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation Book PDF

Author : Charles Collot,Pierre Raphaël,Jeremie Szeftel
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 52,7 Mb
Release : 2019-09-05
Category : Electronic
ISBN : 9781470436261

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On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation by Charles Collot,Pierre Raphaël,Jeremie Szeftel Pdf

The authors consider the energy super critical semilinear heat equation The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data using energy bounds. The whole scheme draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.

Superlinear Parabolic Problems

Pavol Quittner,Philippe Souplet
Superlinear Parabolic Problems Book PDF

Author : Pavol Quittner,Philippe Souplet
Publisher : Springer Science & Business Media
Page : 593 pages
File Size : 45,5 Mb
Release : 2007-12-16
Category : Mathematics
ISBN : 9783764384425

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Superlinear Parabolic Problems by Pavol Quittner,Philippe Souplet Pdf

This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature.

Partial Differential Equations arising from Physics and Geometry

Mohamed Ben Ayed,Mohamed Ali Jendoubi,Yomna Rébaï,Hasna Riahi,Hatem Zaag
Partial Differential Equations arising from Physics and Geometry Book PDF

Author : Mohamed Ben Ayed,Mohamed Ali Jendoubi,Yomna Rébaï,Hasna Riahi,Hatem Zaag
Publisher : Cambridge University Press
Page : 471 pages
File Size : 48,7 Mb
Release : 2019-05-02
Category : Mathematics
ISBN : 9781108431637

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Partial Differential Equations arising from Physics and Geometry by Mohamed Ben Ayed,Mohamed Ali Jendoubi,Yomna Rébaï,Hasna Riahi,Hatem Zaag Pdf

Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.

Nonlinear Optics in Telecommunications

Thomas Schneider
Nonlinear Optics in Telecommunications Book PDF

Author : Thomas Schneider
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 52,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783662089965

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Nonlinear Optics in Telecommunications by Thomas Schneider Pdf

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

Massimo Cicognani,Daniele Del Santo,Alberto Parmeggiani,Michael Reissig
Anomalies in Partial Differential Equations Book PDF

Author : Massimo Cicognani,Daniele Del Santo,Alberto Parmeggiani,Michael Reissig
Publisher : Springer Nature
Page : 469 pages
File Size : 53,5 Mb
Release : 2021-02-03
Category : Mathematics
ISBN : 9783030613464

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Anomalies in Partial Differential Equations by Massimo Cicognani,Daniele Del Santo,Alberto Parmeggiani,Michael Reissig Pdf

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.

Mathematical Theory of Scattering Resonances

Semyon Dyatlov,Maciej Zworski
Mathematical Theory of Scattering Resonances Book PDF

Author : Semyon Dyatlov,Maciej Zworski
Publisher : American Mathematical Soc.
Page : 634 pages
File Size : 42,9 Mb
Release : 2019-09-10
Category : Frequencies of oscillating systems
ISBN : 9781470443665

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Mathematical Theory of Scattering Resonances by Semyon Dyatlov,Maciej Zworski Pdf

Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.