Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres
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Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres
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Author : J.-M. Delort
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-06
Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres written by J.-M. Delort 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 2015-02-06 with Mathematics categories.
The Hamiltonian ∫X(∣∂tu∣2+∣∇u∣2+m2∣u∣2)dx, defined on functions on R×X, where X is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial expressions depending on first order derivatives of u. The associated PDE is then a quasi-linear Klein-Gordon equation. The author shows that, when X is the sphere, and when the mass parameter m is outside an exceptional subset of zero measure, smooth Cauchy data of small size ϵ give rise to almost global solutions, i.e. solutions defined on a time interval of length cNϵ−N for any N. Previous results were limited either to the semi-linear case (when the perturbation of the Hamiltonian depends only on u) or to the one dimensional problem. The proof is based on a quasi-linear version of the Birkhoff normal forms method, relying on convenient generalizations of para-differential calculus.
Global Existence Of Small Amplitude Solutions For A Model Quadratic Quasilinear Coupled Wave Klein Gordon System In Two Space Dimension With Mildly Decaying Cauchy Data
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Author : A. Stingo
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-27
Global Existence Of Small Amplitude Solutions For A Model Quadratic Quasilinear Coupled Wave Klein Gordon System In Two Space Dimension With Mildly Decaying Cauchy Data written by A. Stingo 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 2023-11-27 with Mathematics categories.
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Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle
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Author : Massimiliano Berti
language : en
Publisher: Springer
Release Date : 2018-11-02
Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle written by Massimiliano Berti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-02 with Mathematics categories.
The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Endoscopic Classification Of Representations Of Quasi Split Unitary Groups
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Author : Chung Pang Mok
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-09
Endoscopic Classification Of Representations Of Quasi Split Unitary Groups written by Chung Pang Mok 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 2015-04-09 with Mathematics categories.
In this paper the author establishes the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.
Diagonalizing Quadratic Bosonic Operators By Non Autonomous Flow Equations
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Author : Volker Bach
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-10
Diagonalizing Quadratic Bosonic Operators By Non Autonomous Flow Equations written by Volker Bach 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 2016-03-10 with Mathematics categories.
The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket-Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.
Stability Of Kam Tori For Nonlinear Schr Dinger Equation
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Author : Hongzi Cong
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-25
Stability Of Kam Tori For Nonlinear Schr Dinger Equation written by Hongzi Cong 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 2016-01-25 with Mathematics categories.
The authors prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrödinger equation subject to Dirichlet boundary conditions , where is a real Fourier multiplier. More precisely, they show that, for a typical Fourier multiplier , any solution with the initial datum in the -neighborhood of a KAM torus still stays in the -neighborhood of the KAM torus for a polynomial long time such as for any given with , where is a constant depending on and as .
Numerical Approximations Of Stochastic Differential Equations With Non Globally Lipschitz Continuous Coefficients
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Author : Martin Hutzenthaler
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26
Numerical Approximations Of Stochastic Differential Equations With Non Globally Lipschitz Continuous Coefficients written by Martin Hutzenthaler 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 2015-06-26 with Mathematics categories.
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method. These moment bounds are then used to prove strong convergence of the proposed schemes. Finally, the authors illustrate their results for several SDEs from finance, physics, biology and chemistry.
On The Theory Of Weak Turbulence For The Nonlinear Schrodinger Equation
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Author : M. Escobedo
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-27
On The Theory Of Weak Turbulence For The Nonlinear Schrodinger Equation written by M. Escobedo 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 2015-10-27 with Mathematics categories.
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
Stability Of Line Solitons For The Kp Ii Equation In Mathbb R 2
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Author : Tetsu Mizumachi
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-27
Stability Of Line Solitons For The Kp Ii Equation In Mathbb R 2 written by Tetsu Mizumachi 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 2015-10-27 with Mathematics categories.
The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as . He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward . The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.