Related papers: Partially Exact Controllability of Semilinear Heat…
In this study, we propose a robust control strategy for a counter-current heat exchanger. The primary objective is to regulate the outlet temperature of one fluid stream by manipulating the flow rate of the second counter-current fluid…
This paper deals with the approximate controllability for the semilinear heat equation in one space dimension. Our aim is to provide an estimate of the cost of the control.
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…
A quantum thermal device based on three nearest-neighbor coupled spin-1/2 systems controlled by the magnetic field is proposed. We systematically study the steady-state thermal behaviors of the system. When the two terminals of our system…
Semilinear parabolic systems with bi-linear nonlinearities cover a lot of applications and their optimal control leads to relatively simple optimality conditions. An example is the incompressible Navier-Stokes system for homogeneous fluids,…
A tunable and balanced heat interferometer is proposed and analyzed. The device consists of two superconductors linked together to form a double-loop interrupted by three Josephson junctions coupled in parallel. Both superconductors are…
The semilinear heat equation with non-instantaneous impulses \textbf{(NII)}, memory, and delay is considered and its approximate controllability is obtained. This is done by employing a technique that avoids fixed point theorems and pulls…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…
In this work we analyse the small-time reachability properties of a nonlinear parabolic equation, by means of a bilinear control, posed on a torus of arbitrary dimension $d$. Under a saturation hypothesis on the control operators, we show…
We demonstrate control over heat flow in an N-terminal molecular junction. Using simple model Hamiltonians we show that the heat current through two terminals can be tuned, switched, and amplified, by the temperature and coupling parameters…
We present a unified description of heat flow in two-terminal hybrid quantum systems. Using simple models, we analytically study nonlinear aspects of heat transfer between various reservoirs: metals, solids, and spin baths, mediated by the…
This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the…
In the paper, problems of controllability, approximate controllability, reachability and approximate reachability are studied for the control system $w_t=w_{xx}$, $w(0,\cdot)=u$, $x>0$, $t\in(0,T)$, where $u\in L^\infty(0,T)$ is a control.…
In this paper we consider a multidimensional semilinear reaction-diffusion equation and we obtain at any arbitrary time an approximate controllability result between nonnegative states using as control term the reaction coefficient, that is…
The paper deals with exact null-controllability problem for a linear control system consisting of two serially connected abstract control systems. Controllability conditions are obtained. Applications to the exact null-controllability for…
We study thermal transport along the edge of a small chiral-spin-liquid device coupled to two Ising-chain reservoirs, a platform suitable for quantum-engineered systems. Adiabatically switching on the tunnel couplings to the reservoirs…
We study heat transport in quantum spin systems analytically and numerically. First, we demonstrate that heat current through a two-level quantum spin system can be modulated from zero to a finite value by tuning a magnetic field. Second,…
In many practical applications of control theory some constraints on the state and/or on the control need to be imposed. In this paper, we prove controllability results for semilinear parabolic equations under positivity constraints on the…
We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every…