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Related papers: Two-term spectral asymptotics in linear elasticity

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Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…

Spectral Theory · Mathematics 2007-11-16 Natalia O. Babych , Ilia V. Kamotski , Valery P. Smyshlyaev

We prove Cwikel-Lieb-Rosenbljum and Lieb-Thirring type bounds on the discrete spectrum of a two-body pair operator and calculate spectral asymptotics for the eigenvalue moments and the local spectral density in the pseudo-relativistic…

Mathematical Physics · Physics 2007-05-23 Semjon Vugalter , Timo Weidl

We study the asymptotic behavior of homeomorphic solutions of the Beltrami equation with different conditions on the dilatation at infinity in this paper.

Complex Variables · Mathematics 2015-05-12 O. Afanasieva , R. Salimov

In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…

Functional Analysis · Mathematics 2007-05-23 Jochen Brüning , Matthias Lesch

This article is concerned with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The…

Analysis of PDEs · Mathematics 2021-04-26 Roberta Bianchini , Roberto Natalini

In this paper, we prove a cocycle version of marked length spectrum rigidity. There are two consequences. The first is marked length pattern rigidity for arithmetic hyperbolic locally symmetric manifolds. The second is strengthen marked…

Dynamical Systems · Mathematics 2025-08-19 Yanlong Hao

We study notions of isotopy and concordance for Riemannian metrics on manifolds with boundary and, in particular, we introduce two variants of the concept of minimal concordance, the weaker one naturally arising when considering certain…

Differential Geometry · Mathematics 2024-02-14 Alessandro Carlotto , Chao Li

We consider the discrete spectrum of the Dirichlet Laplacian on a manifold consisting of two adjacent parallel strips or planar layers coupled by a finite number N of windows in the common boundary. If the windows are small enough, there is…

funct-an · Mathematics 2020-01-29 Pavel Exner , Simeon Vugalter

Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg-de Vries equation posed on a finite interval $\left[0, 2\pi \sqrt{7/3}\right]$. The equation comes with a Dirichlet boundary condition at…

Analysis of PDEs · Mathematics 2016-04-06 Shuxia Tang , Jixun Chu , Peipei Shang , Jean-Michel Coron

The aim of this study is to find asymptotic expressions of eigenvalues and eigenfunctions of a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition. Applications of…

Classical Analysis and ODEs · Mathematics 2013-02-20 Erdoğan Şen

For strictly entropic Riemann shock solutions of strictly hyperbolic systems of balance laws, we prove that exponential spectral stability implies large-time asymptotic orbital stability. As a preparation, we also prove similar results for…

Analysis of PDEs · Mathematics 2022-07-27 Grégory Faye , L. Miguel Rodrigues

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this…

Analysis of PDEs · Mathematics 2011-11-29 Le Xuan Truong , Le Thi Phuong Ngoc , Alain Pham Ngoc Dinh , Nguyen Thanh Long

An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…

Analysis of PDEs · Mathematics 2017-04-20 G. Buttazzo , G. Cardone , S. A. Nazarov

We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive $\delta'$ interaction supported by a smooth surface in $\R^3$, either infinite and asymptotically planar, or compact and closed. Its second term is…

Mathematical Physics · Physics 2019-12-10 Pavel Exner , Michal jex

Generalizing the result of Li and Tam for the hyperbolic spaces, we prove an existence theorem on the Dirichlet problem for harmonic maps with $C^1$ boundary conditions at infinity between asymptotically hyperbolic manifolds.

Differential Geometry · Mathematics 2014-12-01 Kazuo Akutagawa , Yoshihiko Matsumoto

In this paper, the asymptotics of the spectral data (eigenvalues and weight numbers) are obtained for the higher-order differential operators with distribution coefficients and separated boundary conditions. Additionally, we consider the…

Spectral Theory · Mathematics 2022-08-30 Natalia P. Bondarenko

This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system of linear partial differential equations. The aim is to…

Spectral Theory · Mathematics 2016-12-13 Zhirayr Avetisyan , Yan-Long Fang , Dmitri Vassiliev

The paper deals with an integrodifferential operator which models numerous phenomena in superconductivity, in biology and in viscoelasticity. Initialboundary value problems with Neumann, Dirichlet and mixed boundary conditions are analyzed.…

Mathematical Physics · Physics 2016-11-02 M. De Angelis

We give an expression, in terms of boundary spectral functions, for the spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its domain is determined by local boundary conditions, and the manifold is of product type.…

High Energy Physics - Theory · Physics 2008-11-26 C. G. Beneventano , E. M. Santangelo , A. Wipf

We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We…

Differential Geometry · Mathematics 2007-05-23 P. T. Chrusciel , R. Bartnik