**Financial support through the following projects:**

UIDB/00297/2020

UID/MAT/00297/2019

UID/MAT/00297/2013

PEst-OE/MAT/UI0297/2014

PEst-OE/MAT/UI0297/2011

Wednesday, 10 December 2014, 2:00 p.m.

Lecturer: Max Souza, Universidade Federal Fluminense

Title: "Conservative Parabolic Problems"

Local: Room 1.6, Edifício VII

Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: Well posed parabolic problems are typically dissipative, and hence no form of conservation law is to be expected-except when dealing with Neumann problems. However parabolic problems where some form of conservation law is specified, instead of a boundary condition, have been studied since at least the sixties in the last century, and are now becoming increasingly popular. In particular, such type of problems appear naturally when characterising the probability density of some evolutionary processes. We will identify a suitable subclass of uniformly parabolic operators where a complete theory for such problems can be developed in one space dimension. In the sequel, we will then show how certain degenerated problems can also be treated along similar lines by means of a perturbation approach. This is joint work with Olga Danilkina and Fabio Chalub.