Manuel González-Burgos

On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient

We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of

Controllability results for cascade systems of m coupled parabolic PDEs by one control force

{\mathbb R}^N

Existence of Insensitizing Controls for a Semilinear Heat Equation with a Superlinear Nonlinearity

with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term

A Local Result on Insensitizing Controls for a Semilinear Heat Equation with Nonlinear Boundary Fourier Conditions

f( y, \nabla y)

Controllability results for linear viscoelastic fluids of the Maxwell and Jeffreys kinds

grows slower than

Insensitizing controls for a semilinear heat equation with a superlinear nonlinearity

|y| \log^{3/2}(1+ |y| + |\nabla y|) + |\nabla y| \log^{1/2}(1+ |y| + |\nabla y|)

Sharp estimates of the one-dimensional boundary control cost for parabolic systems and application to the N-dimensional boundary null controllability in cylindrical domains

at infinity (generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method.

Some Controllability Results for Linear Viscoelastic Fluids

In this paper we will analyze the controllability properties of a linear coupled parabolic system of m equations when a unique distributed control is exerted on the system. We will see that, when a cascade system is considered, we can prove a global Carleman inequality for the adjoint system which bounds the global integrals of the variable φ = (φ1, . . . , φm) ∗ in terms of a unique localized variable. As a consequence, we will obtain the null controllability property for the system with one control force. Mathematics Subject Classification (2000). 93B05, 93B07, 35K50.

Controllability results for discontinuous semilinear parabolic partial differential equations

Abstract In this paper we consider a semilinear heat equation (in a bounded domain Ω of ℝ N ) with a nonlinearity that has a superlinear growth at infinity. We prove the existence of a control, with support in an open set ω ⊂ Ω, that insensitizes the L 2 − norm of the observation of the solution in another open subset 𝒪 ⊂ Ω when ω ∩ 𝒪 ≠ ∅, under suitable assumptions on the nonlinear term f(y) and the right hand side term ξ of the equation. The proof, involving global Carleman estimates and regularizing properties of the heat equation, relies on the sharp study of a similar linearized problem and an appropriate fixed-point argument. For certain superlinear nonlinearities, we also prove an insensitivity result of a negative nature. The crucial point in this paper is the technique of construction of L r -controls (r large enough) starting from insensitizing controls in L 2.

Controllability results for some nonlinear coupled parabolic systems by one control force

In this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form