475 research outputs found
Hitting times and periodicity in random dynamics
We prove quenched laws of hitting time statistics for random subshifts of
finite type. In particular we prove a dichotomy between the law for periodic
and for non-periodic points. We show that this applies to random Gibbs
measures
Carleman estimates for elliptic operators with complex coefficients Part II: transmission problems
We consider elliptic transmission problems with complex coefficients across
an interface. Under proper transmission conditions, that extend known
conditions for well-posedness, and sub-ellipticity we derive microlocal and
local Carleman estimates near the interface. Carleman estimates are weighted a
priori estimates of the solutions of the elliptic transmission problem. The
weight is of exponential form, exp( {\phi}) where can be taken as
large as desired. Such estimates have numerous applications in unique
continuation, inverse problems, and control theory. The proof relies on
microlocal factorizations of the symbols of the conjugated operators in
connection with the sign of the imaginary part of their roots. We further
consider weight functions where {\phi} = exp(), with
acting as a second large paremeter, and we derive estimates where the
dependency upon the two parameters, and , is made explicit.
Applications to unique continuation properties are given.Comment: 58 page
Carleman estimates and controllability results for the one-dimensional heat equation with {\em BV} coefficients
International audienceWe derive global Carleman estimates for one-dimensional linear parabolic operators \d_t \pm \d_x(c \d_x) with a coefficient with bounded variations. These estimates are obtained by approximating by piecewise regular coefficients, c_\eps, and passing to the limit in the Carleman estimates associated to the operators defined with c_\eps. Such estimates yield results of controllability to the trajectories for a classe of {\em semilinear} parabolic equations
On the convergence of some products of Fourier integral operators
An approximation Ansatz for the operator solution, , of a hyperbolic first-order pseudodifferential equation, \d_z + a(z,x,D_x) with , is constructed as the composition of global Fourier integral operators with complex phases. We prove a convergence result for the Ansatz to in some Sobolev space as the number of operators in the composition goes to , with a convergence of order , if the symbol is in \Con^{0,\alpha} with respect to the evolution parameter . We also study the consequences of some truncation approximations of the symbol in the construction of the Ansatz
Geometric control condition for the wave equation with a time-dependent observation domain
We characterize the observability property (and, by duality, the
controllability and the stabilization) of the wave equation on a Riemannian
manifold with or without boundary, where the observation (or control)
domain is time-varying. We provide a condition ensuring observability, in terms
of propagating bicharacteristics. This condition extends the well-known
geometric control condition established for fixed observation domains. As one
of the consequences, we prove that it is always possible to find a
time-dependent observation domain of arbitrarily small measure for which the
observability property holds. From a practical point of view, this means that
it is possible to reconstruct the solutions of the wave equation with only few
sensors (in the Lebesgue measure sense), at the price of moving the sensors in
the domain in an adequate way.We provide several illustrating examples, in
which the observationdomain is the rigid displacement in of a fixed
domain, withspeed showing that the observability property depends both on
and on the wave speed. Despite the apparent simplicity of some of
ourexamples, the observability property can depend on nontrivial
arithmeticconsiderations
Saint-Claud – Déviation RD961
Identifiant de l'opération archéologique : 203946 Date de l'opération : 2009 (EX) Le diagnostic archéologique réalisé dans le cadre du projet de déviation de Saint-Claud n’a pas révélé beaucoup de traces d’occupations. Seule l’une d’elles a pu être datée. Il s’agit de deux grandes fosses, peut-être d’extraction, dont le remplissage a livré une centaine de restes de céramiques et un fragment de bracelet en lignite attribués à la fin du premier âge du Fer. Une demi-douzaine de fosses, beaucoup ..
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