This article establishes the controllability to the trajectories of a reaction-diffusion-advection system describing predator–prey model by using distributed controls acting on a single equation with the no-flux boundary conditions. We first prove the exact null controllability of an associated linearized problem by establishing an observability estimate, derived from a global Carleman type inequality, for the adjoint system. The proof of the nonlinear problem relies on the suitable regularity of the control and Kakutani’s fixed point theorem.

This paper is concerned with the exact null controllability of certain semilinear Black–Scholes type equations in a bounded interval of with Neumann boundary conditions. The control is assumed to be distributed along a subset ω of I. First, we prove the exact null controllability of an associated linearized problem by establishing the observability estimate derived from a Carleman type inequality which is the key result for the whole theory. Then, the exact null controllability of the nonlinear problem is discussed using the infinite-dimensional Kakutani fixed point theorem.

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 this result is successfully used with some estimates for parabolic equation in L^k spaces together with classical fixed point theorem, to prove the null controllability of the nonlinear model.