Veja as informações das próximas palestras do mês de março dos Seminários de Análise/EDP.
A primeira palestra será ministrada pelo aluno de doutorado Gerardo Huaroto (UFRJ).
Data: 16/03/2017 (quinta-feira)
Título: The IBVP for a fractional type degenerated heat equation
Resumo: The main purpose is to study the existence of solutions for an initial-boundary value problem (IBVP) driven by a degenerated fractional heat type equation.
 L. Caffarelli and J.L. Vazquez, Nonlinear Porous Medium Flow with Fractional Potential Pressure Arch. Rational Mech. Anal. 202(2011) 537-565.
 Capella, A.; Davila, J.; Dupaigne, L.; Sire, Y. Regularity of radial extremal solutions for some non local semilinear equations Preprint, arXiv:1004.1906.
A segunda palestra será ministrada pela prof. Juliana Pimentel (UFABC)
Data: 23/03/2017 (quinta-feira)
Título: Longtime behavior of reaction-diffusion equations with infinite-time blow-up
Resumo: We account for the longtime behavior of solutions for a class of reaction-diffusion equations. In particular, we address those with global well-posedness but exhibiting low-up in infinite time. The existence of unbounded trajectories requires the introduction of some objects interpreted as equilibria at infinity, yielding a more complex orbit structure than that appearing on dissipative systems. Under this setting, we still manage to extend known results and obtain a complete decomposition for the related unbounded lobal attractor. This is based on joint works with C. Rocha and A. N. Carvalho.
A terceira palestra será ministrada pelo prof. Alvaro Coutinho (UFRJ)
Data: 30/03/2017 (quinta-feira)
Título: A Residual Based Variational Multiscale Model for Sediment Transport: Towards the Simulation of Non-Dilute Turbidity Currents
Numerical models can help to push forward the knowledge about complex dynamic physical systems. The modern approach to doing that involves detailed mathematical models. Turbidity currents are a kind of particle-laden flows that are a very complex natural phenomenon. In a simple way, they are turbulent driven flows generated between fluids with small density differences carrying particles. They also are one mechanism responsible for the deposition of sediments on the seabed. A detailed understanding of this phenomenon, ncluding uncertainties , may offer new insight to help geologists to understand reservoir formation, a strategic knowledge in oil exploration. We present a finite element residual-based variational multiscale formulation applied to the numerical simulation of particle-laden flows in a Eulerian-Eulerian framework. Thus, the mathematical model esults from the incompressible Navier-Stokes equation combined with an advection-diffusion transport equation. When sediment concentrations are high enough, rheological empirical laws close the model, describing how sediment concentrations influence the mixture viscosity . The aim of this work is to investigate the effects on the flow dynamics of some these empirical laws. We use two configurations for numerical experiments . The first is a lock-exchange configuration in a tank and the second employs a channel with sustained current. Both numerical experiments are inspired in complex laboratory tests. We show how turbulent structures and quantities of interest, such as sediment deposition, are affected by the different empirical rheological laws. This is a first attempt towards model selection in particle-laden flows with complex rheological laws.
 G. M. Guerra, S. Zio, J. J. Camata, R. N. Elias, M. Mattoso, P. L. B. Paraizo, A. L. G. A. Coutinho, F. A. Rochinha, Uncertainty quantification in numerical simulation of particle-laden flows, Computational Geosciences 20(1): 265-281, 2016.
 I. M. Krieger and T.J. Dougherty, A mechanism for non-Newtonian flow in suspensions of rigid spheres. Transactions of the Society of Rheology 3: 37-152 (1959).
 R. Manica, Sediment Gravity Flows: Study Based on Experimental Simulations, Chapter 13, Hydrodynamics – Natural Water Bodies, Prof. Harry Schulz (Ed.), InTech, 2012.