O Colóquio do Departamento de Matemática, a ser realizado hoje (12) às 16h na sala 209 do Departamento de Matemática da UFPE, terá como tema “A brief introduction to discontinuities in Hamilton-Jacobi equations and related control problems”. O colóquio será ministrado pelo professor Emmanuel Chasseigne, da Université de Tours na França.

Resumo

In 1983, the introduction of the notion of viscosity solutions by Crandall and Lions solved the main questions concerning first-order Hamilton-Jacobi equations, both for stationary and evolution cases. The theory was soon after extended for second-order elliptic and parabolic, possibly degenerate, fully non-linear partial differential equations. The immediate success of the notion of viscosity solutions came from both its simplicity but also universality, while it was fitting perfectly with the applications to deterministic control problems, differential games, front propagations, image analysis etc. But despite all these positive points, there was little weakness: the theory only applies with maximal efficiency when solutions are continuous and, even more important, when the Hamiltonians in the equations are continuous. Thus, in the period 1990-2010, several attempts were made to GO further in the understanding of Hamilton-Jacobi equations with discontinuities. And even more recently, several authors developed more advanced tools in the context of equations on networks. The aim of this talk is to present in a quite non-technical way several ideas about this story, and to present some new approaches, especially in the context of control problems.

Mais informações
Departamento de Matemática da UFPE
(81) 2126.7650