Sufficient conditions for controllability of neutral functional integrodifferential systems in Banach spaces with initial condition in the phase space are established. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

A new form of the coprime polynomial fraction $C\left(s\right)F{\left(s\right)}^{-1}$ of a transfer function matrix $G\left(s\right)$ is presented where the polynomial matrices $C\left(s\right)$ and $F\left(s\right)$ have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state- space model and Markov matrices $HB$, $HAB$, ...

In this paper we prove the existence of mild solutions and the controllability for semilinear differential inclusions with nonlocal conditions. Our results extend some recent theorems.

In this paper we study a linear population dynamics model. In this model, the birth process is described by a nonlocal term and the initial distribution is unknown. The aim of this paper is to use a controllability result of the adjoint system for the computation of the density of individuals at some time $T$.

We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed...

In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of $ℝ$ with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients. Then...

The goal of this note is to present the results of the references [5] and [4]. We study the null controllability of the parabolic equations associated with the Grushin-type operator ${\partial }_x^2+{\left|x\right|}^{2\gamma }{\partial }_y^2$ ($\gamma \>0$) in the rectangle $(x,y)\in (-1,1)\times (0,1)$ or with the Kolmogorov-type operator $v^{\gamma }{\partial }_{x}f+{\partial }_v^{2}f$ ($\gamma \in \{1,2\}$) in the rectangle $(x,v)\in 𝕋\times (-1,1)$, under an additive control supported in an open subset $\omega$ of the space domain.We prove that the Grushin-type equation is null controllable in any positive time for $\gamma \<1$ and that there is no time for which it is null controllable for $\gamma \>1$....

We study the null controllability of the parabolic equation associated with the Grushin-type operator $A={\partial }_x^2+{\left|x\right|}^{2\gamma }{\partial }_{\gamma }^2,(\gamma >0)$, in the rectangle $\Omega =(-1,1)\times (0,1)$, under an additive control supported in an open subset $\omega$ of $\Omega$. We prove that the equation is null controllable in any positive time for $\gamma <1$ and that there is no time for which it is null controllable for $\gamma >1$. In the transition regime $\gamma =1$ and when $\omega$ is a strip $\omega =(a,b)\times (0,1)(0<a,b\le 1)$), a positive minimal time is required for null controllability. Our approach is based on the fact that, thanks to the particular...

The internal and boundary exact null controllability of nonlinear convective heat equations with homogeneous Dirichlet boundary conditions are studied. The methods we use combine Kakutani fixed point theorem, Carleman estimates for the backward adjoint linearized system, interpolation inequalities and some estimates in the theory of parabolic boundary value problems in Lk.