Seminário de Análise (Centro de Matemática e Aplicações, Linha EDAN)

22-03-2010

Quarta-feira, 24 de Março de 2010, 12 horas

Título: Constrained Reaction-Diffusion and Transport Systems: the N-membranes and Multiphase Problems

Orador: José Francisco Rodrigues, Universidade de Lisboa/CMAF

Local: Sala de Seminários, 2º piso, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Resumo: We analyse vector valued diffusion and transport equations with a class of constraints of unilateral and bilateral type. Using the variational inequality approach we characterize explicitly the associated Lagrange multipliers by reducing the problems to semi-linear systems coupled through the characteristic functions of the coincident sets of the N-membranes problem, analogously to the obstacle problem. In collaboration with Lisa Santos, we obtain new results to the system associated with the Gibbs simplex for multiphase problems. We also discuss the stability of the solutions and their coincident sets, in particular, the asymptotic behaviour in time for the respective evolution problems.