Por Benoît Merlet (Laboratoire Paul Painlevé, Université de Lille).

Por Clément Cancès (Inria Lille - Nord Europe).

Abstract: We present an original model for immiscible two-phase mixtures. This model can be interpreted as the generalised gradient flow of the same energy as for the classical degenerate Canh-Hilliard model, but for a different geometry. Our model is shown to dissipate faster. Existence of weak solutions is established based on the convergence of a JKO semi discretization (joint work with Flore Nabet and Daniel Matthes).

Por Mário Edmundo (FCUL e CMAFcIO, Universidade de Lisboa).

Por Juan Luis Vázquez (Universidad Autónoma de Madrid).

Nonlocality plays now an important role in the mathematical modelling of diffusion phenomena. The talk presents work on the existence, regularity and typical behaviour of solutions of nonlinear fractional elliptic and parabolic equations, posed in the whole space or in bounded domains. Attention is given to functional aspects, to the boundary behaviour, and to the long time asymptotics. Work with different collaborators will be mentioned.

Por Mário Edmundo (FCUL e CMAFcIO, Universidade de Lisboa).

Por Khompysh Khonatbek (al-Farabi Kazakh national university).

Abstract: In this talk the initial-boundary value problems for modified Kelvin-Voigt equations with p,q-Laplace will be considered. The unique solvability and the quality properties as blow-up in a finite time and large time behaviour of the weak solution will be proved.

Por Alexander Nazarov (PDMI RAS and St. Petersburg University).

Por Boris Zilber (Oxford University).

Por Silvius Klein (Pontifícia Universidade Católica do Rio de Janeiro).

Por Stephan Klaus (M. F. I. Oberwolfach).