On the asymptotic behavior of the discrete spectrum of the Dirichlet and Neumann problems for the Laplace-Beltrami operator on a regular polyhedron in the Lobachevskii space

1990 ◽  
Vol 24 (1) ◽  
pp. 18-25 ◽  
Author(s):  
B. M. Levitan ◽  
L. B. Parnovskii
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Spectrum ◽  
Beltrami Operator ◽  
Regular Polyhedron ◽  
Neumann Problems ◽  
Lobachevskii Space

scholarly journals Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides

2012 ◽  
Vol 11 (2) ◽  
pp. 629-646 ◽  
Author(s):  
Carlos Jerez-Hanckes ◽  
Jean-Claude Nédélec
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Spectrum ◽  
Electromagnetic Fields ◽  
Three Dimensions ◽  
Guided Modes ◽  
Open Waveguides ◽  
Radiation Conditions

AbstractWe extend classic Sommerfeld and Silver-Müller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If X= (x1,x2,x3)ϵℝ3, with x3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region ∣x3∣ > ∣∣x∣γ, for γϵ(1/4,1/2) and x large. For ∣x3∣ < ∣∣x∣∣γ and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

Dirichlet Laplacian in a thin twisted strip

2019 ◽  
Vol 30 (02) ◽  
pp. 1950006
Author(s):  
Alessandra A. Verri
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Spectrum ◽  
Laplacian Operator ◽  
Two Dimensional ◽  
Effective Operator ◽  
Dirichlet Laplacian

Let [Formula: see text] be a two-dimensional, infinite and twisted strip in [Formula: see text]. Consider [Formula: see text] the Dirichlet Laplacian operator in [Formula: see text]. At first, we find the effective operator when the transversal sections of [Formula: see text] tend to zero. Then, assuming that [Formula: see text] is thin enough, we show some situations where the discrete spectrum [Formula: see text] is nonempty; an asymptotic behavior for the eigenvalues is also found. In particular, we study the case where the twisted effect “grows” at infinity.

scholarly journals A zeta function connected with the eigenvalues of the Laplace-Beltrami operator on the fundamental domain of the modular group

1984 ◽  
Vol 96 ◽  
pp. 167-174 ◽  
Author(s):  
Akio Fujii
Keyword(s):  
Zeta Function ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Fundamental Domain ◽  
Modular Group ◽  
Beltrami Operator

Let ; … run over the eigenvalues of the discrete spectrum of the Laplace-Beltrami operator on L2(H/yΓ), where H is the upper half of the complex plane and we take Γ = PSL(2, Z). It is well known that Let a be a positive number. Here we are concerned with the zeta function defined by

CONVERGENCE RESULTS FOR A PHASE TRANSITION MODEL WITH VANISHING MICROSCOPIC ACCELERATION

2004 ◽  
Vol 14 (03) ◽  
pp. 375-392 ◽  
Author(s):  
GIOVANNA BONFANTI ◽  
FABIO LUTEROTTI
Keyword(s):  
Phase Transition ◽  
Asymptotic Behavior ◽  
Transition Model ◽  
Well Posedness ◽  
Macroscopic Level ◽  
Neumann Problems ◽  
Convergence Results ◽  
Recent Phase

A recent phase transition model, proposed by Frémond, is based on the consideration that the microscopic movements are responsible for the phase transition at the macroscopic level. A last version of the model, accounting also for the microscopic accelerations has been investigated in Ref. 4, where well-posedness results are established for related Cauchy–Neumann problems. The aim of this paper is the study of the asymptotic behavior of the solution to one of the above problems, as the power of the microscopic acceleration forces goes to zero.

The asymptotic behavior of the spectral function of an operator in Lp with discrete spectrum

1994 ◽  
Vol 69 (3) ◽  
pp. 1065-1067
Author(s):  
V. A. Sadovnichii ◽  
V. V. Dubrovskii ◽  
A. V. Nagornyi
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Function ◽  
Discrete Spectrum
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