Boundary local null-controllability of the Kuramoto–Sivashinsky equation

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...

Local Boundary Controllability for the Semilinear Plate Equation

The problem of local controllability for the semilinear plate equation with Dirichlet boundary conditions is studied. By making use of Schauder’s fixed point theorem and the inverse function theorem, we prove that this system is locally controllable under a super-linear assumption on the nonlinearity, that is, the initial states in a small neighborhood of 0 in a certain function space can be dr...

Null Controllability of a Nonlinear Heat Equation

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...

The L∞-null controllability of parabolic equation with equivalued surface boundary conditions

In this paper, we obtain the L∞−null controllability of the parabolic equation with equivalued surface boundary conditions in Ω× [0, T ]. The control is supported in the product of an open subset of Ω and a subset of [0, T ] with positive measure. The main result is obtained by the method of Lebeau-Robianno-type iteration, based on a new estimate for partial sum of the eigenfunctions of the ell...