Boundary null controllability of degenerate heat equation as the limit of internal controllability

Null Controllability of a Nonlinear Heat Equation

On the minimal time null controllability of the heat equation

In this work, two-dimensional microeconomic models with three controls are created and investigated. The models describe a manufacturer producing a consumer good and a retailer that buys his product in order to resell it for profit. Two types of differential hierarchical games will be applied in order to model the interactions of manufacturer and retailer. We will consider the difficult case in...

Boundary local null-controllability of the Kuramoto-Sivashinsky equation

We prove that the Kuramoto-Sivashinsky equation is locally controllable in 1D and in 2D with one boundary control. Our method consists in combining several general results in order to reduce the nullcontrollability of this nonlinear parabolic equation to the exact controllability of a linear beam or plate system. This improves known results on the controllability of Kuramoto-Sivashinsky equatio...

Null Controllability of the Heat Equation with Boundary Fourier Conditions: the Linear Case

Abstract. In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form ∂y ∂n + β y = 0. We consider distributed controls with support in a small set and nonregular coefficients β = β(x, t). For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classi...

Finite Dimensional Null Controllability for the Semilinear Heat Equation

ABSTRACI’. We study a finite dimensional version of the null controllability problem for semilinear heat equations in bounded domains R of R” with Dirichlet boundary conditions. The control acts on any open an non-empty subset of R. The question under consideration is the following: given an initial state, a control time t = 2’ and a finite dimensional subspace E of L”(n), is there a control su...