scholarly journals Essential spectrum and Weyl asymptotics for discrete Laplacians

2015 ◽  
Vol 24 (3) ◽  
pp. 563-624 ◽  
Author(s):  
Michel Bonnefont ◽  
Sylvain Golénia
Keyword(s):  
Essential Spectrum ◽  
Weyl Asymptotics ◽  
Discrete Laplacians

scholarly journals Discrete Laplacians on general polygonal meshes

2011 ◽  
Vol 30 (4) ◽  
pp. 1-10 ◽  
Author(s):  
Marc Alexa ◽  
Max Wardetzky
Keyword(s):  
Polygonal Meshes ◽  
Discrete Laplacians

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

scholarly journals On Gromov's theorem andL 2-Hodge decomposition

2004 ◽  
Vol 2004 (1) ◽  
pp. 25-44 ◽  
Author(s):  
Fu-Zhou Gong ◽  
Feng-Yu Wang
Keyword(s):  
Essential Spectrum ◽  
Vector Bundles ◽  
Functional Inequality ◽  
Upper Bounds ◽  
Hodge Decomposition ◽  
Laplace Type

Using a functional inequality, the essential spectrum and eigenvalues are estimated for Laplace-type operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the correspondingL 2-harmonic sections. In particular, some known results concerning Gromov's theorem and theL 2-Hodge decomposition are considerably improved.

Marangoni instability of a thin liquid film heated from below by a local heat source

2003 ◽  
Vol 475 ◽  
pp. 377-408 ◽  
Author(s):  
SERAFIM KALLIADASIS ◽  
ALLA KIYASHKO ◽  
E. A. DEMEKHIN
Keyword(s):  
Free Surface ◽  
Liquid Film ◽  
Discrete Spectrum ◽  
Essential Spectrum ◽  
Marangoni Number ◽  
Thin Liquid Film ◽  
Nonlinear Partial Differential Equations ◽  
Spanwise Direction ◽  
Surface Boundary ◽  
Integral Boundary

We consider the motion of a liquid film falling down a heated planar substrate. Using the integral-boundary-layer approximation of the Navier–Stokes/energy equations and free-surface boundary conditions, it is shown that the problem is governed by two coupled nonlinear partial differential equations for the evolution of the local film height and temperature distribution in time and space. Two-dimensional steady-state solutions of these equations are reported for different values of the governing dimensionless groups. Our computations demonstrate that the free surface develops a bump in the region where the wall temperature gradient is positive. We analyse the linear stability of this bump with respect to disturbances in the spanwise direction. We show that the operator of the linearized system has both a discrete and an essential spectrum. The discrete spectrum bifurcates from resonance poles at certain values of the wavenumber for the disturbances in the transverse direction. The essential spectrum is always stable while part of the discrete spectrum becomes unstable for values of the Marangoni number larger than a critical value. Above this critical Marangoni number the growth rate curve as a function of wavenumber has a finite band of unstable modes which increases as the Marangoni number increases.

Sign in / Sign up

Export Citation Format

Share Document