Lack of Null-Controllability for the Fractional Heat Equation and Related Equations

Null Controllability of a Nonlinear Heat Equation

On the Lack of Null-controllability of the Heat Equation on the Half-line

We consider the linear heat equation on the half-line with a Dirichlet boundary control. We analyze the null-controllability problem. More precisely, we study the class of initial data that may be driven to zero in finite time by means of an appropriate choice of the L2 boundary control. We rewrite the system on the similarity variables that are a common tool when analyzing asymptotic problems....

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...

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...

Approximate controllability and lack of controllability to zero of the heat equation with memory

Abstract In this paper we consider the heat equation with memory in a bounded region Ω ⊂ Rd, d ≥ 1, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of class C1. We examine its controllability properties both under the action of boundary controls or when the controls are distributed in a subregion of Ω. We prove approximate ...