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Spectral asymptotics for nonsmooth singular Green operators
Spectral asymptotics nonsmooth singular Green operators Analysis of PDEs
2012/5/9
Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain \Omega \subset R^n, and more generally they appear in the calcul...
Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit
Spectral stability periodic wave trains Korteweg-de Vries/Kuramoto-Sivashinsky equation Korteweg-de Vries limit
2012/3/1
We study the spectral stability of a family of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation $ \partial_t v+v\partial_x v+\partial_x^3 v+\delta(\partial_x^2 v +\partial_x...
$L^q$ bounds on restrictions of spectral clusters to submanifolds for low regularity metrics
$L^q$ restrictions spectral clusters submanifolds low regularity metrics
2012/3/1
We prove $L^q$ bounds on the restriction of spectral clusters to submanifolds in Riemannian manifolds equipped with metrics of $C^{1,\alpha}$ regularity for $0 \leq \alpha \leq 1$. Our results allow f...
Refined Scattering and Hermitian Spectral Theory for Linear Higher-Order Schrodinger Equations
Higher-order Schrodinger operators rescaled blow-up variables discrete real spectrum asymptotic behaviour nodal sets of solutions
2011/9/9
Abstract: A classification of large-time and finite-time blow-up asymptotics of solutions of the Cauchy problem for higher-order Schr\"odinger equations is performed.
On the spectral properties of L_{+-} in three dimensions
spectral properties three dimensions Analysis of PDEs
2011/8/23
Abstract: This paper is part of the radial asymptotic stability analysis of the ground state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon equations in three dimensions. We demons...
Uniform Estimates of the Prolate Spheroidal Wave Functions and Spectral Approximation in Sobolev Spaces
Uniform Estimates of the Prolate Spheroidal Wave Functions Spectral Approximation Sobolev Spaces
2011/2/22
For fixed c Prolate Spheroidal Wave Functions ψn,c form a basis with remarkable properties
for the space of band-limited functions with bandwith c and have been largely studied and
used after the se...
Spectral estimates for resolvent differences of self-adjoint elliptic operators
Spectral estimates resolvent differences
2011/2/24
The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations.
Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators
Elliptic equations Dirichlet and Neumann boundary conditions stability of eigenvalues
2011/2/25
We prove sharp stability estimates for the variation of the eigenvalues of non-negative self-adjoint elliptic operators of arbitrary even order upon variation of the open sets on which they are define...
Lack of Spectral Gap and Hyperbolicity in Asymptotic Erdös-Renyi Random Graphs
Spectral Gap Hyperbolicity Asymptotic Erdö s-Renyi Random Graphs
2010/12/14
In this work, we prove the absence of a spectral gap for the normalized Laplacian of the Erdos-Renyi random graph G(n; p) when p = d n for d > 1 as n ! 1. We also prove that for any positive the Er...
Spectral Methods in PDE
Spectral Methods PDE
2010/11/30
This is to review some recent progress in PDE. The emphasis is on (energy)supercritical nonlinear Schr¨odinger equations. The methods are applicable to other nonlinear equations.
In this paper, we consider the numerical solution of quasi-parabolic equations of higher order by a spectral method, and propose a computational formula. We give an error estimate of approximate solut...