Detailed programme:
 (5 min)
David Krejcirik:
opening, motivation of the session
Relevance of nonselfadjoint theories in physics,
mathematical complications, etc.
 (15 min)
Petr Siegl:
PTsymmetry versus pseudoHermiticity
 (15 min)
Guy Bouchitte:
Transmission between media with opposite sign dielectric constants and
anomalous resonances
 (15 min)
Lionel Rosier:
Output feedback stabilization of a clampedfree beam
We consider a EulerBernoulli beam, clamped at one extremity and
free at the other, to which are attached a piezoelectric actuator
and a collocated sensor. We are interested in the stability properties
of the system depending on the length/position of the actuator/sensor.
 (15 min)
Sylvain Ervedoza:
Exponential decay of the energy of discrete waves
I will discuss some issues arising in the study of the exponential
stability of the damped wave equation and its discretizations. I
will briefly recall how the exponential decay rate can be measured
for the continuous damped wave equation (which have been obtained in
articles from CoxZuazua in 1d and later by Lebeau in higher
dimension). Then, assuming that the damped wave equation is
exponentially stable (that is, the energy is exponentially decaying),
one can study the stabilization properties of the corresponding
space/time/fullydiscrete schemes. It has been shown recently that in
general, these numerical approximations are NOT uniformly (with
respect to the discretization parameters) exponentially stable.
However, adding a suitable numerical viscosity operator in the
discrete systems, we can correct this phenomenon and guarantee
uniform stabilization properties. But, the uniform exponential decay
rate of the energy of the discrete systems is not known, since it
would require a (asymptotic) spectral theory for the discrete systems
on nonselfadjoint operators. I will also present some numerical
simulations to give some indications of the expected results.
 (10 min)
if there is enough time, otherwise skipped
David Krejcirik:
PTsymmetric waveguides and the lack of variational techniques
In a joint paper with Denis Borisov,
we introduced a planar waveguide
with nonHermitian paritytimesymmetric Robin boundary conditions.
Using perturbation methods, we demonstrated the existence
of real weaklycoupled eigenvalues outside
the essential spectrum provided that the boundary coupling function is
a small perturbation of homogeneous boundary conditions.
An open problem is to show the existence of discrete spectra
by some qualitatives methods,
regardless of the strength of the perturbation.
 (15 min)
if there is enough time, otherwise skipped
Enrique Zuazua:
Remarks on the damped wave equation
