In this review, concerning parabolic equations, we give self-contained descriptions on (1)
derivations of Carleman estimates;(2) methods for applications of the Carleman estimates to …

Abstract Contents Introduction § 1. Statement of the problem. Main results 1.1. Exact
boundary controllability of the Navier-Stokes equations 1.2. Local exact distributed …

In this chapter we present some of the recent progresses done on the problem of
controllability of partial differential equations (PDE). Control problems for PDE arise in many …

In a bounded domain $\Omega\subset\mathbb {R}^ d $ over time interval $(0, T) $, we
consider mean field game equations whose principal coefficients depend on the time and …

We prove Carleman inequalities for a second order parabolic equation when the coefficients
are not bounded and norms of right hand sides are taken in the Sobolev space L 2 (0, T; W …

We study the local exact controllability problem for the Navier-Stokes equations that
describe an incompressible fluid flow in a bounded domain Ω with control distributed in a …

This paper is concerned with the null controllability of systems governed by semilinear
parabolic equations. The control is exerted either on a small subdomain or on a portion of …

In this paper a model reference-based adaptive parameter estimator for a wide class of
hyperbolic distributed parameter systems is considered. The proposed state and parameter …

In these notes we analyze some problems related to the controllability and observability of
partial differential equations and its space semidiscretizations. First we present the problems …

These notes are a written abridged version of a course that both authors have delivered in
the last five years in a number of schools and doctoral programs. Our main goal is to …