A Vector Field Method On The Distorted Fourier Side And Decay For Wave Equations With Potentials
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A Vector Field Method On The Distorted Fourier Side And Decay For Wave Equations With Potentials
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Author : Roland Donninger
language : en
Publisher:
Release Date : 2016
A Vector Field Method On The Distorted Fourier Side And Decay For Wave Equations With Potentials written by Roland Donninger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Differential equations, Parabolic categories.
A Vector Field Method On The Distorted Fourier Side And Decay For Wave Equations With Potentials
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Author : Roland Donninger
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-26
A Vector Field Method On The Distorted Fourier Side And Decay For Wave Equations With Potentials written by Roland Donninger 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 2016-04-26 with Mathematics categories.
The authors study the Cauchy problem for the one-dimensional wave equation ∂2tu(t,x)−∂2xu(t,x)+V(x)u(t,x)=0. The potential V is assumed to be smooth with asymptotic behavior V(x)∼−14|x|−2 as |x|→∞. They derive dispersive estimates, energy estimates, and estimates involving the scaling vector field t∂t+x∂x, where the latter are obtained by employing a vector field method on the “distorted” Fourier side. In addition, they prove local energy decay estimates. Their results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is fundamental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space; see Donninger, Krieger, Szeftel, and Wong, “Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space”, preprint arXiv:1310.5606 (2013).
Layer Potentials And Boundary Value Problems For Second Order Elliptic Operators With Data In Besov Spaces
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Author : Ariel Barton:
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-09-06
Layer Potentials And Boundary Value Problems For Second Order Elliptic Operators With Data In Besov Spaces written by Ariel Barton: 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 2016-09-06 with Mathematics categories.
This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Lp classes. The authors establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given Lp space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.
The Role Of Advection In A Two Species Competition Model A Bifurcation Approach
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Author : Isabel Averill
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-01-18
The Role Of Advection In A Two Species Competition Model A Bifurcation Approach written by Isabel Averill 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 2017-01-18 with Bifurcation theory categories.
The effects of weak and strong advection on the dynamics of reaction-diffusion models have long been studied. In contrast, the role of intermediate advection remains poorly understood. For example, concentration phenomena can occur when advection is strong, providing a mechanism for the coexistence of multiple populations, in contrast with the situation of weak advection where coexistence may not be possible. The transition of the dynamics from weak to strong advection is generally difficult to determine. In this work the authors consider a mathematical model of two competing populations in a spatially varying but temporally constant environment, where both species have the same population dynamics but different dispersal strategies: one species adopts random dispersal, while the dispersal strategy for the other species is a combination of random dispersal and advection upward along the resource gradient. For any given diffusion rates the authors consider the bifurcation diagram of positive steady states by using the advection rate as the bifurcation parameter. This approach enables the authors to capture the change of dynamics from weak advection to strong advection. The authors determine three different types of bifurcation diagrams, depending on the difference of diffusion rates. Some exact multiplicity results about bifurcation points are also presented. The authors' results can unify some previous work and, as a case study about the role of advection, also contribute to the understanding of intermediate (relative to diffusion) advection in reaction-diffusion models.
Direct And Inverse Scattering At Fixed Energy For Massless Charged Dirac Fields By Kerr Newman De Sitter Black Holes
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Author : Thierry Daudé
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-25
Direct And Inverse Scattering At Fixed Energy For Massless Charged Dirac Fields By Kerr Newman De Sitter Black Holes written by Thierry Daudé 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 2017-04-25 with Black holes (Astronomy) categories.
In this paper, the authors study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, they establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. The authors also use the miraculous property (quoting Chandrasekhar)—that the Dirac equation can be separated into radial and angular ordinary differential equations—to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, the authors use this expression of the scattering matrix to study the uniqueness property in the associated inverse scattering problem at fixed energy. Using essentially the particular form of the angular equation (that can be solved explicitly by Frobenius method) and the Complex Angular Momentum technique on the radial equation, the authors are finally able to determine uniquely the metric of the black hole from the knowledge of the scattering matrix at a fixed energy.
Locally Analytic Vectors In Representations Of Locally Adic Analytic Groups
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Author : Matthew J. Emerton
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-13
Locally Analytic Vectors In Representations Of Locally Adic Analytic Groups written by Matthew J. Emerton 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 2017-07-13 with Geometry, Analytic categories.
The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various “radii of analyticity”). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.
Carleman Estimates Observability Inequalities And Null Controllability For Interior Degenerate Nonsmooth Parabolic Equations
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Author : Genni Fragnelli
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-21
Carleman Estimates Observability Inequalities And Null Controllability For Interior Degenerate Nonsmooth Parabolic Equations written by Genni Fragnelli 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 2016-06-21 with Mathematics categories.
The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.
An Inverse Spectral Problem Related To The Geng Xue Two Component Peakon Equation
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Author : Hans Lundmark
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-10-05
An Inverse Spectral Problem Related To The Geng Xue Two Component Peakon Equation written by Hans Lundmark 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 2016-10-05 with Discontinuous functions categories.
The authors solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperis-Procesi equations. Like the spectral problems for those equations, this one is of a ``discrete cubic string'' type-a nonselfadjoint generalization of a classical inhomogeneous string--but presents some interesting novel features: there are two Lax pairs, both of which contribute to the correct complete spectral data, and the solution to the inverse problem can be expressed using quantities related to Cauchy biorthogonal polynomials with two different spectral measures. The latter extends the range of previous applications of Cauchy biorthogonal polynomials to peakons, which featured either two identical, or two closely related, measures. The method used to solve the spectral problem hinges on the hidden presence of oscillatory kernels of Gantmacher-Krein type, implying that the spectrum of the boundary value problem is positive and simple. The inverse spectral problem is solved by a method which generalizes, to a nonselfadjoint case, M. G. Krein's solution of the inverse problem for the Stieltjes string.
Igusa S P Adic Local Zeta Function And The Monodromy Conjecture For Non Degenerate Surface Singularities
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Author : Bart Bories
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-21
Igusa S P Adic Local Zeta Function And The Monodromy Conjecture For Non Degenerate Surface Singularities written by Bart Bories 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 2016-06-21 with Mathematics categories.
In 2011 Lemahieu and Van Proeyen proved the Monodromy Conjecture for the local topological zeta function of a non-degenerate surface singularity. The authors start from their work and obtain the same result for Igusa's p-adic and the motivic zeta function. In the p-adic case, this is, for a polynomial f∈Z[x,y,z] satisfying f(0,0,0)=0 and non-degenerate with respect to its Newton polyhedron, we show that every pole of the local p-adic zeta function of f induces an eigenvalue of the local monodromy of f at some point of f−1(0)⊂C3 close to the origin. Essentially the entire paper is dedicated to proving that, for f as above, certain candidate poles of Igusa's p-adic zeta function of f, arising from so-called B1-facets of the Newton polyhedron of f, are actually not poles. This turns out to be much harder than in the topological setting. The combinatorial proof is preceded by a study of the integral points in three-dimensional fundamental parallelepipeds. Together with the work of Lemahieu and Van Proeyen, this main result leads to the Monodromy Conjecture for the p-adic and motivic zeta function of a non-degenerate surface singularity.
Abelian Properties Of Anick Spaces
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Author : Brayton Gray
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-02-20
Abelian Properties Of Anick Spaces written by Brayton Gray 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 2017-02-20 with Abelian groups categories.
Anick spaces are closely connected with both EHP sequences and the study of torsion exponents. In addition they refine the secondary suspension and enter unstable periodicity. This work describes their -space properties as well as universal properties. Techniques include a new kind on Whitehead product defined for maps out of co-H spaces, calculations in an additive category that lies between the unstable category and the stable category, and a controlled version of the extension theorem of Gray and Theriault (Geom. Topol. 14 (2010), no. 1, 243–275).