相关论文: Approximation of null controls for semilinear heat…

In this paper, we first prove a uniform upper bound on costs of null controls for semilinear heat equations with globally Lipschitz nonlinearity on a sequence of increasing domains, where the controls are acted on an equidistributed set…

We prove that the thickness property is a necessary and sufficient geometric condition that ensures the (rapid) stabilization or the approximate null-controllability with uniform cost of a large class of evolution equations posed on the…

This article is devoted to the analysis of control properties for a heat equation with singular potential $\mu/\delta^2$, defined on a bounded $C^2$ domain $\Omega\subset\mathbb{R}^N$, where $\delta$ is the distance to the boundary…

This paper concerns the global in time existence of solutions for a semilinear heat equation \begin{equation} \tag{P} \label{eq:P} \begin{cases} \partial_t u = \Delta u + f(u), &x\in \mathbb{R}^N, \,\,\, t>0, \\[3pt] u(x,0) = u_0(x) \ge 0,…

We consider the equation $(\partial_t + \rho(\sqrt{-\Delta}))f(t,x) = \mathbf 1_\omega u(t,x)$, $x\in \mathbb R$ or $\mathbb T$. We prove it is not null-controllable if $\rho$ is analytic on a conic neighborhood of $\mathbb R_+$ and…

In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb R_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a…

We explore further controllability problems through a standard least square approach. By setting up a suitable error functional $E$, and putting $m(\ge0)$ for the infimum, we interpret approximate controllability by asking $m=0$, while…

In this paper we study partial-approximate controllability of semilinear nonlocal fractional evolution equations in Hilbert spaces. By using fractional calculus, variational approach and approximating technique, we give the approximate…

We consider a semi-linear heat equation with Dirichlet boundary conditions and globally Lipschitz nonlinearity, posed on a bounded domain of R^N (N $\in$ N *), assumed to be an unknown perturbation of a reference domain. We are interested…

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…

We prove that a free boundary semilinear heat equation with Stefan boundary condition and radially symmetric data is locally null controllable. The strategy involves reducing the problem to the corresponding one-dimensional formulation and…

We study the null controllability of three parabolic equations. The control is acting only on one of the three equations. The three equations are coupled by means of two cubic nonlinearities. The linearized control system around 0 is not…

In this paper we investigate null-controllable initial states of the half heat equation controlled from a sub-arc $\omega$ of the unit circle. We also study the projection on positive frequencies of the half-heat equation. For this…

In this note, we give an elementary proof of the lack of null controllability for the heat equation on the half line by employing the machinery inherited by the unified transform, known also as the Fokas method. This approach also extends…

We analyze controllability properties for the one-dimensional heat equation with singular inverse-square potential $$ u_t-u_{xx}-\frac{\mu}{x^2}u=0,\;\;\; (x,t)\in(0,1)\times(0,T).$$ For any $\mu<1/4$, we prove that the equation is null…

This paper discusses the approximate controllability of a fractional differential control problem driven by a nonlinear hemivariational inequality in a Hilbert space. First, we prove the existence of a mild solution for a fractional control…

In this work, we establish a Carleman inequality for the heat equation with Fourier boundary conditions of the form $\partial_\nu y+by=f1_\gamma$, where the control acts on a small portion $\gamma$ of the boundary. We apply this inequality…

In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial…

We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when…

In this paper, we investigate the null controllability of nonlinear wave systems. Initially, we employ a combination of the Galerkin method and a fixed point theorem to establish the null controllability for semi-linear wave equations with…