Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential

2020 ◽  
Vol 268 (8) ◽  
pp. 4102-4118 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Eigenvalue Problem ◽  
Continuous Spectrum ◽  
Two Phase ◽  
Unbounded Potential

scholarly journals A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces

2009 ◽  
Vol 104 (1) ◽  
pp. 132 ◽  
Author(s):  
Mihai Mihailescu ◽  
Vicentiu Radulescu
Keyword(s):  
Continuous Function ◽  
Eigenvalue Problem ◽  
Continuous Spectrum ◽  
Sobolev Spaces ◽  
Differential Operators ◽  
Smooth Boundary ◽  
Nonlinear Eigenvalue Problem ◽  
Sufficient Conditions ◽  
Open Set ◽  
Quasilinear Problem

We study the nonlinear eigenvalue problem $-(\mathrm{div} (a(|\nabla u|)\nabla u)=\lambda|u|^{q(x)-2}u$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega$ is a bounded open set in ${\mathsf R}^N$ with smooth boundary, $q$ is a continuous function, and $a$ is a nonhomogeneous potential. We establish sufficient conditions on $a$ and $q$ such that the above nonhomogeneous quasilinear problem has continuous families of eigenvalues. The proofs rely on elementary variational arguments. The abstract results of this paper are illustrated by the cases $a(t)=t^{p-2}\log (1+t^r)$ and $a(t)= t^{p-2} [\log (1+t)]^{-1}$.

scholarly journals Shape derivative for a two-phase eigenvalue problem and optimal configurations in a ball

2009 ◽  
Vol 27 ◽  
pp. 311-321 ◽  
Author(s):  
Carlos Conca ◽  
Rajesh Mahadevan ◽  
Leon Sanz
Keyword(s):  
Eigenvalue Problem ◽  
Shape Derivative ◽  
Two Phase ◽  
Optimal Configurations

An Extremal Eigenvalue Problem for a Two-Phase Conductor in a Ball

2008 ◽  
Vol 60 (2) ◽  
pp. 173-184 ◽  
Author(s):  
Carlos Conca ◽  
Rajesh Mahadevan ◽  
León Sanz
Keyword(s):  
Eigenvalue Problem ◽  
Two Phase

Instability growth rate of two-phase mixing layers from a linear eigenvalue problem and an initial-value problem

2010 ◽  
Vol 22 (9) ◽  
pp. 092104 ◽  
Author(s):  
Anne Bagué ◽  
Daniel Fuster ◽  
Stéphane Popinet ◽  
Ruben Scardovelli ◽  
Stéphane Zaleski
Keyword(s):  
Growth Rate ◽  
Eigenvalue Problem ◽  
Initial Value Problem ◽  
Instability Growth Rate ◽  
Mixing Layers ◽  
Initial Value ◽  
Two Phase ◽  
Phase Mixing ◽  
Linear Eigenvalue Problem ◽  
Instability Growth

A global branch of positive solutions above the continuous spectrum for problems with indefinite nonlinearities

1996 ◽  
Vol 126 (3) ◽  
pp. 465-482 ◽  
Author(s):  
Tassilo Küpper ◽  
Achilles Tertikas
Keyword(s):  
Eigenvalue Problem ◽  
Weight Function ◽  
Continuous Spectrum ◽  
Positive Solutions ◽  
Nontrivial Solutions ◽  
Superlinear Growth ◽  
Indefinite Nonlinearities ◽  
Neumann Eigenvalue ◽  
Half Axis ◽  
Global Branch

We prove the existence and bifurcation of a global branch of positive solutions for a nonlinear Neumann eigenvalue problem on the half axis [0, ∞). The nonlinearity is assumed to have a superlinear growth multiplied by a weight function changing sign. This leads to the existence of nontrivial solutions above the continuous spectrum of the linearised problem.

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

Effect of Shock Loading on the Microstructure of Uniloy 326

1974 ◽  
Vol 32 ◽  
pp. 504-505
Author(s):  
K. P. Staudhammer ◽  
L. E. Murr
Keyword(s):  
Grain Size ◽  
Shock Loading ◽  
Current Investigation ◽  
Two Phase ◽  
05 C ◽  
Shock Deformation ◽  
Heat Treated

The effect of shock loading on a variety of steels has been reviewed recently by Leslie. It is generally observed that significant changes in microstructure and microhardness are produced by explosive shock deformation. While the effect of shock loading on austenitic, ferritic, martensitic, and pearlitic structures has been investigated, there have been no systematic studies of the shock-loading of microduplex structures.In the current investigation, the shock-loading response of millrolled and heat-treated Uniloy 326 (thickness 60 mil) having a residual grain size of 1 to 2μ before shock loading was studied. Uniloy 326 is a two phase (microduplex) alloy consisting of 30% austenite (γ) in a ferrite (α) matrix; with the composition.3% Ti, 1% Mn, .6% Si,.05% C, 6% Ni, 26% Cr, balance Fe.

Exsolution and inversion in pigeonite from the Whin Sill, Northern England

1978 ◽  
Vol 36 (1) ◽  
pp. 474-475
Author(s):  
P.P.K. Smith
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Homogeneous Nucleation ◽  
Silicate Mineral ◽  
Antiphase Boundaries ◽  
Two Phase ◽  
Primitive Form ◽  
The Core ◽  
Nucleation Mechanisms ◽  
And Inversion

Grains of pigeonite, a calcium-poor silicate mineral of the pyroxene group, from the Whin Sill dolerite have been ion-thinned and examined by TEM. The pigeonite is strongly zoned chemically from the composition Wo8En64FS28 in the core to Wo13En34FS53 at the rim. Two phase transformations have occurred during the cooling of this pigeonite:- exsolution of augite, a more calcic pyroxene, and inversion of the pigeonite from the high- temperature C face-centred form to the low-temperature primitive form, with the formation of antiphase boundaries (APB's). Different sequences of these exsolution and inversion reactions, together with different nucleation mechanisms of the augite, have created three distinct microstructures depending on the position in the grain.In the core of the grains small platelets of augite about 0.02μm thick have farmed parallel to the (001) plane (Fig. 1). These are thought to have exsolved by homogeneous nucleation. Subsequently the inversion of the pigeonite has led to the creation of APB's.

Sign in / Sign up

Export Citation Format

Share Document