Resultados de controlabilidade para equações parabólicas: equação do calor como limite da equação da onda e equação de Stokes com restrição

Abstract

In this thesis, we study null controllability problems related to the wave, heat, and Stokes equations. Firstly, we establish uniform null controllability for a dissipative wave equation, and as a limit, we achieve null controllability for the heat equation. To accomplish this, we combine a spectral analysis and Carleman inequalities. In the second problem, our focus is on null controllability for the Stokes equation under certain constraints. More specifically, we aim to drive the solution to zero while maintaining orthogonality to a given finite-dimensional space.