MAI 2003
SEMINAIRE
D’ANALYSE NUMERIQUE
ET
EQUATIONS AUX DERIVEES PARTIELLES DE LYON
Mardi 13 mai :
14h15, salle 112, Bât Doyen Jean Braconnier, UCBL
Y.
IL'YASOV (Université de la Rochelle)
Titre : "On
non local calculation of bifurcations for the equatioins
of variational form. Application to inhomogeneous
elliptic boundary value problems"
Résumé : Let $W$ be a Banach
space and $I_{\lambda}$ a real functional of class
$C^1(W\setminus \{0\})$ which depends on the real parameter
$\lambda$.
It is considered
the problem of the existence of critical points of
$I_{\lambda}$ on $W$. To solve the problem, firstly it has to
be
determined a
suitable interval $(\lambda_j, \lambda_{j+1}) \subseteq
\Real$ in such a
way that in the further investigations it enables us to
find the
critical points of $I_{\lambda}$ on $W$ for $\lambda \in
(\lambda_j, \lambda_{j+1})$. In general, the points $\lambda_j$ are
bifurcation values
for the branch of the critical points of
$I_{\lambda}$. In linear cases, the calculation of these
points
$\lambda_j$ is a subject of the spectral theory. However in
nonlinear
cases, it is
absent such a general theory; usually, the sufficient
interval $(\lambda_j,\lambda_{j+1}) \subseteq
\Real$ are possibly
guessed by
using a priori observations.
In the talk it will
present a method for a constructive calculation of
the
sufficient intervals for the given functional $I_{\lambda}$ on
Banach space with respect
to the considered parameter $\lambda$.
We illustrate the
method on the example of a class of inhomogeneous
elliptic
boundary value problems with indefinite nonlinearities and on
the class
of the generalized Ambrosetti-Brezis-Cerami problem
with
convex-concave nonlinearities.
Mardi 20 mai : 14h15, salle 112, Bât Doyen Jean Braconnier,
UCBL
I.
GRUAIS (IRMAR, Université Rennes I)
Titre : "Homogénéisation d'un mélange de
fluides"
15h45, salle 112, Bât Doyen Jean Braconnier,
UCBL
P. CANNARSA (Université de Rome II)
Titre : Representation
of Equilibrium Solutions to the Table Problem for Growing Sandpiles".
Résumé : In the
Dynamical theory of granular matter the so-called table problem consists in
studying the evolution of a heap of matter poured continuously onto a bounded
domain D of the Euclidean plane. The mathematical description of the table
problem, at an equilibrium configuration, can be reduced to a boundary value
problem for a system of partial differential equations. The analysis of such a
system, also connected with other mathematical models such as the Monge-kantorovich problem, is the object of this seminar.
Our main result is an integral representation formula for the solution in terms
of boundary curvature and of the normal distance to the cut locus.
Mardi 27 mai : 14h15, sale 112, Bât Doyen Jean
Braconnier, UCBL
C. CASTRO
(Universidad Polytechnica de Madrid)
Titre : "Controllability
of the heat equation from an oscillating lower dimensional manifold".