Applied Mathematics and Numerical Analysis Seminar 

We compute bound on effective properties of homogenizedmaterials in conduction and linear elasticity. We use $H$-measures,following the original ideas and exposition of Luc Tartar. After having recovered classical Hashin-Shtrikman simple bounds wepropose to deal with coupled bounds in conduction.

Iremos estudar a propagação do erro temporal na integração numérica de ondas solitárias que são solução da equação $u_t+u_x+(1/2)u_x^2-u_{xxt}=0$, usando uma interpretação geométrica dessas ondas como equilíbrios relativos. Mostraremos que o crescimento do erro é linear para métodos que preservam quantidades invariantes do problema e quadrático para métodos não conservativos. Serão apresentados alguns resultados numéricos.

In this talk we will consider the incompressible Navier-Stokes equations, where the extra stress is replaced by an operator which is induced by a suitable potential with $p$-growth. Hereby we restrict ourselves to the three dimensional space periodic case. First of all we will consider a small trick to increase the regularity of the velocity to $L^\infty(I, W^{1,6(p-1)}(\Omega))$. With this gained regularity in mind we will attack the problem of existence of strong solutions (for small times) for small values of $p$, namely $p >7/5$.