Anna Doubova

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

SOME CONTROL RESULTS FOR SIMPLIFIED ONE-DIMENSIONAL MODELS OF FLUID-SOLID INTERACTION

{\mathbb R}^N

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

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

On the control of viscoelastic Jeffreys fluids

f( y, \nabla y)

Rotated weights in global Carleman estimates applied to an inverse problem for the wave equation

grows slower than

Some Controllability Results for Linear Viscoelastic Fluids

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

Extinction-time for stochastic population models

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.

EXACT CONTROLLABILITY TO TRAJECTORIES FOR SEMILINEAR HEAT EQUATIONS WITH DISCONTINUOUS DIFFUSION COEFFICIENTS

We analyze the null controllability of a one-dimensional nonlinear system which models the interaction of a fluid and a particle. This can be viewed as a first step in the control analysis of fluid-solid systems. The fluid is governed by the Burgers equation and the control is exerted at the boundary points. We present two main results: the global null controllability of a linearized system and the local null controllability of the nonlinear original model. The proofs rely on appropriate global Carleman inequalities, observability estimates and fixed point arguments.

On the controllability of the heat equation with nonlinear boundary Fourier conditions

Abstract In this Note, we analyze the null and approximate controllability of some linear systems that can be used, at first approximation, to describe the behavior of some viscoelastic fluids. We consider mainly the distributed control case, with an arbitrarily small support of the control function. We deduce null and approximate controllability results for fluids of the Maxwell kind and an approximate controllability result for fluids of the Jeffreys kind.

Some geometric inverse problems for the linear wave equation

Abstract This paper is devoted to analyzing the control of vicoelastic fluids of the Jeffreys kind, also known as Oldroyd models. We will present the interesting problems, with special emphasis in the difficulties that they involve. Then, we will consider appropriate linear approximations and we will establish some partial approximate-finite dimensional controllability results in an arbitrarily small time, with distributed or boundary controls supported by arbitrarily small sets. The proofs rely on some specific unique continuation properties which are implied by the structure of the solutions.