Recent Advances in Kinetic Theory and their connection to Nonlinear PDEs, Functional Inequalities and Applied Probability

Amit Einav
University of Cambridge

Abstract: Kinetic theory is the field of mathematics that deals with systems of many objects. In recent years, this field has seen an awakening and renewed interest, and has been the focus of attention of many prominent mathematicians. In this talk we will discuss recent advances in the field, mainly in relation to the Boltzmann-Nordheim equation and Kac’s Model, and tie them to the fields of Nonlinear PDEs, Functional Inequalities and Applied Probability.

Uma criterização intrínseca para a bijectividade de operadores de Hilbert relacionados com os sistemas de Friedrichs

Jorge Fragoso

Abstract: Neste seminário do Mestrado de Matemática serão expostos resultados recentes, de A. Ern, J-L. Guermond e G. Caplain <Comm. P. D.E. 32 (2007). 317-341> sobre uma nova abordagem Hibertiana à teoria de Friedrich para os sistemas simétricos positivos, que visa caracterizar as condições de fronteira admissíveis. Inclui-se a apresentação de aplicações a problemas clássicos nos limites para equações com derivadas parciais.

Equilibrium and Euler-Lagrange equation for hyperelastic materials

Elvira Zappale
Universidade de Salerno

Abstract: By means of duality we prove existence and uniqueness of equilibrium for energies described by integral functionals which fail to be convex. This analysis is motivated by some physical models of elastic materials (cf. for istance [2, 4]) and the techniques generalize the methods first introduced in [5, 1]. A suitable Euler Lagrange equation characterizing the minimizers is derived.

Joint work with G. Carita and G. Pisante