1,720,963 research outputs found
L∞ bounds of Steklov eigenfunctions and spectrum stability under domain variation
No full textWe give a practical tool to control the L∞-norm of the Steklov eigenfunctions in a Lipschitz domain in terms of the norm of the BV-trace operator. The norm of this operator has the advantage to be characterized by purely geometric quantities. As a consequence, we give a spectral stability result for the Steklov eigenproblem under geometric domain perturbations and several examples where stability occurs. In particular we deal with geometric domains which are not equi-Lipschitz, like vanishing holes, merging sets, approximations of inner peaks
On the local solvability for a nonlinear weakly hyperbolic equation with analytic coefficients.
No full textNonlinear Stability and Existence of Two-Dimensional Compressible Current-Vortex Sheets
Full text linkWe are concerned with the nonlinear stability and existence of two-dimensional current-vortex sheets in ideal compressible magnetohydrodynamics. This is a nonlinear hyperbolic initial-boundary value problem with a characteristic free boundary. It is well-known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions that yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. We first identify a sufficient condition ensuring the weak stability of the linearized current-vortex sheets problem. Under this stability condition for the background state, we show that the linearized problem obeys an energy estimate in anisotropic weighted Sobolev spaces with a loss of derivatives. Based on the weakly linear stability results, we then establish the local-in-time existence and nonlinear stability of current-vortex sheets by a suitable Nash-Moser iteration, provided that the stability condition is satisfied at each point of the initial discontinuity. This result gives a new confirmation of the stabilizing effect of sufficiently strong magnetic fields on Kelvin-Helmholtz instabilities
-limit of periodic obstacles. Special issue dedicated to Antonio Avantaggiati on the occasion of his 70th birthday
No full textStability of an incompressible plasma–vacuum interface with displacement current in vacuum
No full textWe study the free boundary problem for a plasma–vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better understand the influence of the electric field in vacuum, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. Under the necessary and sufficient stability condition for a planar interface found earlier by Trakhinin, we prove an energy a priori estimate for the linearized constant coefficient problem. The process of derivation of this estimate is based on various methods, including a secondary symmetrization of the vacuum Maxwell equations, the derivation of a hyperbolic evolutionary equation for the interface function, and the construction of a degenerate Kreiss-type symmetrizer for an elliptic-hyperbolic problem for the total pressure
On well-posedness of the plasma-vacuum interface problem with displacement current in vacuum
Full text linkWe consider the plasma-vacuum interface problem in ideal incompressible magneto-hydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better understand the influence of the electric field in vacuum we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. Under the necessary and sufficient stability condition for a planar interface found earlier by Trakhinin, we prove an energy a priori estimate for the linearized constant coefficient problem. The process of derivation of this estimate is based on various methods, including a secondary symmetrization of the vacuum Maxwell equations, the derivation of a hyperbolic evolutionary equation for the interface function and the construction of a degenerate Kreiss-type symmetrizer for an elliptic-hyperbolic problem for the total pressure
An existence result for optimal obstacles.
No full textAbstractWe consider the optimization problem min{F(g):g∈X(Ω)}, whereF(g) is a variational energy associated to the obstaclegand the classX(Ω) of admissible obstacles is given byX(Ω)={g:Ω→R:g⩽ψonΩ, ∫Ωgdx=c} withψ∈W1,p0(Ω) andc∈R fixed. Generally, this problem does not have a solution and it may happen that the “optimal” obstacle is of relaxed form. Under a monotonicity assumption onF, we prove the existence of a non-relaxed optimal obstacle in the familyX(Ω) through a new method based on the notions ofγandwγ-convergences
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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