13 research outputs found
Homogenization of Steklov spectral problems with indefinite density function in perforated domains
The asymptotic behavior of second order self-adjoint elliptic Steklov
eigenvalue problems with periodic rapidly oscillating coefficients and with
indefinite (sign-changing) density function is investigated in periodically
perforated domains. We prove that the spectrum of this problem is discrete and
consists of two sequences, one tending to -{\infty} and another to +{\infty}.
The limiting behavior of positive and negative eigencouples depends crucially
on whether the average of the weight over the surface of the reference hole is
positive, negative or equal to zero. By means of the two-scale convergence
method, we investigate all three cases.Comment: 24 pages. arXiv admin note: substantial text overlap with
arXiv:1106.390
Uniform resolvent convergence for strip with fast oscillating boundary
In a planar infinite strip with a fast oscillating boundary we consider an
elliptic operator assuming that both the period and the amplitude of the
oscillations are small. On the oscillating boundary we impose Dirichlet,
Neumann or Robin boundary condition. In all cases we describe the homogenized
operator, establish the uniform resolvent convergence of the perturbed
resolvent to the homogenized one, and prove the estimates for the rate of
convergence. These results are obtained as the order of the amplitude of the
oscillations is less, equal or greater than that of the period. It is shown
that under the homogenization the type of the boundary condition can change
A survey of topics related to Functional Analysis and Applied Sciences
This survey is the result of investigations suggested by recent publications on functional analysis and applied sciences. It contains short accounts of the above theories not usually combined in a single document and completes the work of D. Huet 2017. The main topics which are dealt with involve spectrum and pseudospectra of partial differential equations, Steklov eigenproblems, harmonic Bergman spaces, rotation number and homeomorphisms of the circle, spectral flow, homogenization. Applications to different types of natural sciences such as echosystems, biology, elasticity, electromagnetisme, quantum mechanics, are also presented. It aims to be a useful tool for advanced students in mathematics and applied sciences
SPECTRAL ANALYSIS AND PROBLEMS WITH OSCILLATING CONSTRAINTS IN THE THEORY OF HOMOGENIZATION
We study the asymptotic behavior of eigenpairs in an elliptic spectral problem on a periodically perforated domain, with Fouirer type boundary condition.
We consider the homogenization of the Dirichlet intergral for n-dimensional curves, taking their values on oscillating constraints, converging to smooth manifolds
Asymptotic analysis of mathematical models for elastic composite media
SIGLEAvailable from British Library Document Supply Centre-DSC:DXN016255 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Steklov problems in perforated domains with a coefficient of indefinite sign
We consider homogenization of Steklov spectral problem for a divergence form elliptic operator in periodically perforated domain under the assumption that the spectral weight function changes sign. We show that the limit behaviour of the spectrum depends essentially on wether the average of the weight function over the boundary of holes is positive, or negative or equal to zero. In all these cases we construct the asymptotics of the eigenpairs
Electromagnetic Waves
This book is dedicated to various aspects of electromagnetic wave theory and its applications in science and technology. The covered topics include the fundamental physics of electromagnetic waves, theory of electromagnetic wave propagation and scattering, methods of computational analysis, material characterization, electromagnetic properties of plasma, analysis and applications of periodic structures and waveguide components, and finally, the biological effects and medical applications of electromagnetic fields