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The current article examines the approximate controllability problem for non-instantaneous impulsive fractional evolution equations of order $1<\alpha<2$ with state-dependent delay in separable reflexive Banach spaces. In order to establish…

Optimization and Control · Mathematics 2021-06-30 S. Arora , Manil T. Mohan , J. Dabas

Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…

Optimization and Control · Mathematics 2020-06-02 Domènec Ruiz-Balet , Enrique Zuazua

Various controllability conditions have been obtained by researchers for heterogeneous networked systems with linear dynamics. However, the literature for nonlinear, heterogeneous networked systems is comparatively less. In this paper we…

Optimization and Control · Mathematics 2024-12-18 Aleena Thomas , Abhijith Ajayakumar , Raju K. George

In this work we investigate a phase field model for damage processes in two-dimensional viscoelastic media with nonhomogeneous Neumann data describing external boundary forces. In the first part we establish global-in-time existence,…

Analysis of PDEs · Mathematics 2016-09-16 M. Hassan Farshbaf-Shaker , Christian Heinemann

This paper deals with the boundary controllability of inviscid incompressible fluids for which thermal effects are important. They will be modeled through the so called Boussinesq approximation. In the zero heat diffusion case, by adapting…

Optimization and Control · Mathematics 2024-02-13 Enrique Fernández-Cara , Maurício C. Santos , Diego A. Souza

In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a parabolic equation where the diffusion coefficient is the product of a degenerate function in space and a nonlocal term. We consider one control…

Optimization and Control · Mathematics 2025-09-25 Juan Límaco , João Carlos Barreira , Suerlan Silva , Luis P. Yapu

This paper addresses the problem of input-to-state stabilization for a class of parabolic equations with time-varying coefficients, as well as Dirichlet and Robin boundary disturbances. By using time-invariant kernel functions, which can…

Optimization and Control · Mathematics 2024-06-18 Yongchun Bi , Jun Zheng , Guchuan Zhu

In this article we study the minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems when all the controls are acting on the same side of the boundary. We establish an explicit and easy-to-compute…

Optimization and Control · Mathematics 2019-02-22 Long Hu , Guillaume Olive

We are concerned about the controllability of a general linear hyperbolic system of the form $\partial_t w (t, x) = \Sigma(x) \partial_x w (t, x) + \gamma C(x) w(t, x) $ ($\gamma \in \mR$) in one space dimension using boundary controls on…

Optimization and Control · Mathematics 2018-12-05 Jean-Michel Coron , Hoai-Minh Nguyen

We consider optimal control problems governed by systems describing the flow of an incompressible second grade fluid with Dirichlet boundary conditions. We prove the existence of an optimal solution, derive the corresponding necessary…

Optimization and Control · Mathematics 2016-01-21 Nadir Arada

Let $\Delta$ be the Dirichlet Laplacian on the interval $(0,\pi)$. The null controllability properties of the equation $$u_{tt}+\Delta^2 u+\rho (\Delta)^\alpha u_t=F(x,t)$$ are studied. Let $T>0$, and assume initial conditions $(u^0,u^1)\in…

Optimization and Control · Mathematics 2024-01-29 Sergei Avdonin , Julian Edward , Sergei Ivanov

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…

Analysis of PDEs · Mathematics 2025-11-17 Juan Límaco , Luis P. Yapu

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

Analysis of PDEs · Mathematics 2015-06-09 Ugur G. Abdulla

In this paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak in "New blow-up rates for…

Optimization and Control · Mathematics 2013-09-10 Pierre Lissy

Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…

Optimization and Control · Mathematics 2025-11-18 Manuel Rissel , Marius Tucsnak

This manuscript is concerned with the approximate controllability of fractional nonlinear differential equations with nonlocal conditions of order $1<q<2$ in Banach spaces. As far as we know, few articles have investigated this issue. The…

Optimization and Control · Mathematics 2024-11-19 Ahmed Aberqi , Zoubida Echchaffani , Touria Karite

This article contributes to a framework for a computational indirect method based on the Pontryagin maximum principle to efficiently solve a class of state constrained time-optimal control problems in the presence of a time-dependent flow…

Optimization and Control · Mathematics 2022-06-30 Roman Chertovskih , Nathalie T. Khalil , Fernando Lobo Pereira

For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…

solv-int · Physics 2008-02-03 B. Shklyar

In this contribution, we study an optimal control problem for the celebrated nonlocal Cahn-Hilliard equation endowed with the singular Flory-Huggins potential in the three-dimensional setting. The control enters the governing state system…

Optimization and Control · Mathematics 2024-01-19 Andrea Poiatti , Andrea Signori

In this paper, we prove an approximate controllability result for the linearized Boussinesq system around a fluid at rest, in a two dimensional channel, when the control acts only on the temperature, through the upper boundary.

Optimization and Control · Mathematics 2020-01-07 Kévin Le Balc'h