talks of the seminar (11:00,
Room Sousa Pinto):
mathematical analysis of viscous and incompressible fluids "
Hermenegildo Oliveira (FCT,
University of Algarve and CMAF, University of Lisbon)
Abstract: In this talk, we shall consider
the initial-boundary value problem for modelling
isothermal ﬂows of incompressible ﬂuids with shear stress depending
Firstly, we shall give an historical
perspective of the evolution of this model of Fluid Mechanics through the
last centuries, starting with a simple, but outstanding, observation by I.
Newton and ending up in the consideration of smart fluids. For all the
considered problems, we will discuss the existence and uniqueness of weak
solutions. In this particular, we will highlight the cases that still
remain open in spite of all the research that have been done in this field
of Mathematics. In a different topic, we will also discuss about the
important issue of the extinction in a finite time of the corresponding
Behaviour of optimal shapes for
spectral optimisation problems "
Pedro Freitas (Department of Mathematics, Faculdade de Motricidade Humana, UTL)
Abstract: We consider the behaviour
of optimal shapes for the kth eigenvalue of the
Laplace operator under different boundary conditions and measure restrictions.
Our studies combine a rigorous analytic approach with numerical
simulations, allowing us to cover the whole range from low to high
This is based on joint work with P.R.S. Antunes, D. Bucur and J.
Susana Moura (CMUC,
University of Coimbra)