Brazil. 18.12.2018. The PhD student of the Chair of Computational Mathematics, Miguel Nuñez, has successfully presented his PhD thesis ‘Some aspects of controllability for non-linear parabolic and hyperbolic equations‘ in Universidade Federal Fluminense, Río of Janeiro, Brazil.
Abstract of the thesis: The main goals of this thesis is the theoretical study of control in parabolic non-linear equations, for example, we have the study of the null control of a system with turbulence and coupling of type Boussinesq. In this case we will eliminate the number of scalar controls and work on an arbitrary domain. We will also study the null local controllability of an one-dimensional nonlinear parabolic system. On the other hand we have the study of the hierarchical control of an equation of heat type with non-linearities in the term of diffusion. Here we will apply Stackelberg-Nash strategies to solve the problem. Finally we will study the exact controllability of a hyperbolic equation with non-local non-linearities.