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Quasi Linear Perturbations Of Hamiltonian Klein Gordon Equations On Spheres
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Book Synopsis Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres by : J.-M. Delort
Download or read book Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres written by J.-M. Delort and published by American Mathematical Soc.. This book was released on 2015-02-06 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 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 by : A. Stingo
Download or read book 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 published by American Mathematical Society. This book was released on 2023-11-27 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle by : Massimiliano Berti
Download or read book Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle written by Massimiliano Berti and published by Springer. This book was released on 2018-11-02 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Boyan Sirakov
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Boyan Sirakov and published by World Scientific. This book was released on 2019-02-27 with total page 5393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Endoscopic Classification of Representations of Quasi-Split Unitary Groups by : Chung Pang Mok
Download or read book Endoscopic Classification of Representations of Quasi-Split Unitary Groups written by Chung Pang Mok and published by American Mathematical Soc.. This book was released on 2015-04-09 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations by : Volker Bach
Download or read book Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations written by Volker Bach and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stability of KAM Tori for Nonlinear Schrödinger Equation by : Hongzi Cong
Download or read book Stability of KAM Tori for Nonlinear Schrödinger Equation written by Hongzi Cong and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 .
Book Synopsis Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients by : Martin Hutzenthaler
Download or read book Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients written by Martin Hutzenthaler and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation by : M. Escobedo
Download or read book On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation written by M. Escobedo and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stability of Line Solitons for the KP-II Equation in $\mathbb {R}^2$ by : Tetsu Mizumachi
Download or read book Stability of Line Solitons for the KP-II Equation in $\mathbb {R}^2$ written by Tetsu Mizumachi and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Moduli of Double EPW-Sextics by : Kieran G. O'Grady
Download or read book Moduli of Double EPW-Sextics written by Kieran G. O'Grady and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of ⋀3C6 modulo the natural action of SL6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3[2] polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds.
Book Synopsis Classification of $E_0$-Semigroups by Product Systems by : Michael Skeide
Download or read book Classification of $E_0$-Semigroups by Product Systems written by Michael Skeide and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.
Book Synopsis Classes of Polish Spaces Under Effective Borel Isomorphism by : Vassilios Gregoriades
Download or read book Classes of Polish Spaces Under Effective Borel Isomorphism written by Vassilios Gregoriades and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the equivalence classes under Δ11 isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of Δ11-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.
Book Synopsis The Fourier Transform for Certain HyperKahler Fourfolds by : Mingmin Shen
Download or read book The Fourier Transform for Certain HyperKahler Fourfolds written by Mingmin Shen and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle representing the Beauville-Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of Hyperkähler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.
Book Synopsis Spectral Means of Central Values of Automorphic L-Functions for GL(2) by : Masao Tsuzuki
Download or read book Spectral Means of Central Values of Automorphic L-Functions for GL(2) written by Masao Tsuzuki and published by American Mathematical Soc.. This book was released on 2015-04-09 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with Green's functions on adele points of considered over a totally real number field, the author elaborates an explicit version of the relative trace formula, whose spectral side encodes the informaton on period integrals of cuspidal waveforms along a maximal split torus. As an application, he proves two kinds of asymptotic mean formula for certain central -values attached to cuspidal waveforms with square-free level.
Book Synopsis Higher Moments of Banach Space Valued Random Variables by : Svante Janson
Download or read book Higher Moments of Banach Space Valued Random Variables written by Svante Janson and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.
Book Synopsis On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System by : Weiwei Ao
Download or read book On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System written by Weiwei Ao and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Click here to view the abstract. IntroductionProof of Theorem 1.1 in the caseProof of Theorem 1.1 in the caseAppendixBibliography
