相关论文: Constructive exact control of semilinear 1D heat e…
The exact distributed controllability of the semilinear wave equation $\partial_{tt}y-\Delta y + g(y)=f \,1_{\omega}$ posed over multi-dimensional and bounded domains, assuming that $g\in C^1(\mathbb{R})$ satisfies the growth condition…
The null distributed controllability of the semilinear heat equation $y_t-\Delta y + g(y)=f \,1_{\omega}$, assuming that $g$ satisfies the growth condition $g(s)/(\vert s\vert \log^{3/2}(1+\vert s\vert))\rightarrow 0$ as $\vert s\vert…
It has been proved by Zuazua in the nineties that the internally controlled semilinear 1D wave equation $\partial_{tt}y-\partial_{xx}y + g(y)=f 1_{\omega}$, with Dirichlet boundary conditions, is exactly controllable in $H^1_0(0,1)\cap…
The exact distributed controllability of the semilinear wave equation $y_{tt}-y_{xx} + g(y)=f \,1_{\omega}$, assuming that $g$ satisfies the growth condition $\vert g(s)\vert /(\vert s\vert \log^{2}(\vert s\vert))\rightarrow 0$ as $\vert…
We consider the semilinear heat equation posed on a smooth bounded domain $\Omega$ of $\mathbb{R}^{N}$ with Dirichlet or Neumann boundary conditions. The control input is a source term localized in some arbitrary nonempty open subset…
We address the exact boundary controllability of the semilinear wave equation $\partial_{tt}y-\Delta y + f(y)=0$ posed over a bounded domain $\Omega$ of $\mathbb{R}^d$. Assuming that $f$ is continuous and satisfies the condition…
The null controllability of the heat equation is known for decades [19,23,30]. The finite time stabilizability of the one dimensional heat equation was proved by Coron--Nguy\^en [13], while the same question for high dimensional spaces…
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…
It is by now well known that the use of Carleman estimates allows to establish the control-lability to trajectories of nonlinear parabolic equations. However, by this approach, it is not clear how to decide whether a given function is…
In this paper, we analyze the controllability properties under positivity constraints on the control or the state of a one-dimensional heat equation involving the fractional Laplacian $(-\Delta)^s$ ($0<s<1$) on the interval $(-1,1)$. We…
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 an exact controllability result for a one-dimensional heat equation with delay in both lower and highest order terms and nonhomogeneous Dirichlet boundary conditions. Moreover, we give an explicit representation of the control…
In the paper, the problems of controllability and approximate controllability are studied for the control system $w_t=\Delta w$, $w_{x_1}(0,x_2,t)=u(t)\delta(x_2)$, $x_1>0$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u\in L^\infty(0,T)$ is a…
In this work we extend a variational method to study the approximate controllability and finite dimensional exact controllability ( finite-approximate controllability) for the semilinear evolution equations in Hilbert spaces. We state a…
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…
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…
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.
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…
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…
This paper deals with the problem of internal null-controllability of a heat equation posed on a bounded domain with Dirichlet boundary conditions and perturbed by a semilinear nonlocal term. We prove the small-time local…