Boundary Null Controllability With Constrained Control for a Nonlinear Two Stroke System: Application to Boundary Sentinel and Identification of Parameters in a Nonlinear Population Dynamics Model

We first prove a new controllability result for a nonlinear two stroke system. The key to solve this controllability problem is an adapted Carleman inequality. Next, the obtained result is used to build a boundary sentinel to identify unknown parameters in a nonlinear population dynamics model with incomplete data.

Boundary Sentinel with Given Sensitivity in Population Dynamics Problem and Parameters Identification

The notion of sentinels with given sensitivity was introduced by J.L.Lions [11] in order to identify parameters in the problem of pollution ruled by a parabolic equation. He proves that the existence of such sentinels is reduced to the solution of exact controllability problem with constraints on the state. In population dynamics model, we reconsider this notion of sentinels in a more general framework. We prove the existence of the boundary sentinels by solving a boundarynull-controllability problem with constraint on the control. Our results use Carleman inequality which is adapted to the constraint.

Simultaneous Null Controllability for Two Stroke Nonlinear Systems: Application to the Sentinel of Detection in Population Dynamics Model with Incomplete Data

This paper deals with the simultaneous null controllability for some nonlinear two stroke systems. We shall solve this problem by transforming the simultaneous null controllability of uncoupled initial systems into a null controllability of a coupled system via a change of variables. This last problem is solved thanks to a global Carleman inequality, appropriates estimates adapted to the system and via some fixed point theorems. The obtained results are used to build a simultaneous sentinel of detection in a population dynamics model with incomplete data.

Accurate estimates of (1+x)1/x involved in Carleman inequality and Keller limit

In this paper, using the Maclaurin series of the functions (1+x)1/x, some inequalities from papers [2] and [5] are generalized. For arbitrary Maclaurin series some general limits of Keller?s type are defined and applying for generalization of some well known results.

Null Controllability of a Nonlinear Dissipative System and Application to the Detection of the Incomplete Parameter for a Nonlinear Population Dynamics Model

We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.

On Unique Continuation for Navier-Stokes Equations

We study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. As a consequence we obtain sufficient conditions on the behavior of the solution at two different timest0=0andt1=1which guarantee the “global” unique continuation of solutions for the Navier-Stokes equations.