186,292 research outputs found
On the local solvability for a nonlinear weakly hyperbolic equation with analytic coefficients.
No full text-limit of periodic obstacles. Special issue dedicated to Antonio Avantaggiati on the occasion of his 70th birthday
No full textPreface
No full textPreface of the special Issue of Discrete and Continuous Dynamical Systems - Series S entitled “Fluid Dynamics and Electromagnetism: Theory and Numerical Approximation
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
On well-posedness of the plasma-vacuum interface problem with displacement current in vacuum
No full textWe 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
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
A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problems
No full textWe prove that if is bounded open subset in the plane and its complement satisfies suitable structural assumptions (for example it has a countable number of connected components), then is dense in for every exponent p between 1 and 2. The main application of this density result is the study of stability under boundary variations for nonlinear elliptic problems under Neumann conditions
Nonlinear Stability and Existence of Two-Dimensional Compressible Current-Vortex Sheets
No full textWe 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
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