相关论文: Memory approximate controllability properties for …

We consider the Cauchy problem for a first-order evolution equation with memory in a finite-dimensional Hilbert space when the integral term is related to the time derivative of the solution. The main problems of the approximate solution of…

We investigate forward and backward problems associated with abstract time-fractional Schr\"odinger equations $\mathrm{i}^\nu \partial_t^\alpha u(t) + A u(t)=0$, $\alpha \in (0,1)\cup (1,2)$ and $\nu\in\{1,\alpha\}$, where $A$ is a…

In this paper, we discuss the approximate controllability for control systems governed by stochastic evolution hemivariational inequalities in Hilbert spaces. The interest in studying this type of equation comes from its application in some…

In the paper, the problems of controllability and approximate controllability are studied for the control system $w_t=\frac{1}{\rho}\left(kw_x\right)_x+\gamma w$, $\left.\left(\sqrt{\frac{k}{\rho}}w_x\right)\right|_{x=0}=u$, $x>0$,…

We consider the three-dimensional ideal MHD system on a domain $\Omega' \subset \mathbb{R}^3$ with a part $\Gamma$ of the boundary~$\partial \Omega$, where we prescribe both $u\cdot n$ and $b\cdot n$, while $u\cdot n = b\cdot n =0$ on…

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 propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…

The current paper initially studies the optimal control of linear $\psi$-Hilfer fractional derivatives with state-dependent control constraints and optimal control for a particular type of cost functional. Then, we investigate the…

We establish sharp regional observability results for solutions of the wave equation in a bounded domain of $\Omega \subset \mathbb{R}^n$, in case where the geometric control condition is not satisfied. Assuming that the waves are observed…

This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…

The paper addresses the problem of optimization of a guaranteed (worst case) result for a control system driven by a controlling side in presence of a dynamical disturbance. The disturbances as functions of time are subject to functional…

We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ Basing on the finite-difference Gr\"{u}nwald-Letnikov…

We consider Schr{\"o}dinger equations with logarithmic nonlinearity and bilinear controls, posed on $\mathbb{T}^d$ or $\mathbb{R}^d$. We prove their small-time global $L^2$-approximate controllability. The proof consists in extending to…

We study the exact null controllability of a class of non-autonomous conformable fractional semi-linear evolution systems with nonlocal initial conditions in Hilbert spaces. The analysis is carried out within the framework of conformable…

Given an elliptic operator~$L$ on a bounded domain~$\Omega \subseteq {\bf R}^n$, and a positive Radon measure~$\mu$ on~$\Omega$, not charging polar sets, we discuss an explicit approximation procedure which leads to a sequence of…

The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the…

In this paper we study $2$nd order $L^\infty$ variational problems, through seeking to minimise a supremal functional involving the Hessian of admissible functions as well as lower-order terms. Specifically, given a bounded domain…

In this paper, we are concerned with the regional boundary controllability of the Riemann-Liouville time fractional diffusion systems of order $\alpha\in (0,1]$. The characterizations of strategic actuators are established when the systems…

In this paper we investigate a discrete approximation in time and in space of a Hilbert space valued stochastic process $\{u(t)\}_{t\in [0,T]}$ satisfying a stochastic linear evolution equation with a positive-type memory term driven by an…

This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative. Some necessary and sufficient conditions…