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In their recent work `Well-posedness, regularity and asymptotic analyses for a fractional phase field system' (Asymptot. Anal. 114 (2019), 93-128; see also the preprint arXiv:1806.04625), two of the present authors have studied phase field…

Analysis of PDEs · Mathematics 2020-05-28 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…

Optimization and Control · Mathematics 2015-01-07 Kenichi Fujishiro

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…

Optimization and Control · Mathematics 2018-05-16 Dario Pighin , Enrique Zuazua

In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…

Systems and Control · Electrical Eng. & Systems 2024-07-04 Gilberto O. Corrêa , Marlon M. López-Flores , Alexandre L. Madureira

In this paper we study the local boundary controllability for a non linear system of two degenerate parabolic equations with a control acting on only one equation. We analyze boundary null controllability properties for the linear system…

Analysis of PDEs · Mathematics 2024-11-11 Margarita Arias , Abdelkarim Hajjaj , Amine Sbai

In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under…

Optimization and Control · Mathematics 2020-12-11 Jean-Michel Coron , Hoai-Minh Nguyen

We consider the problem of controlling parabolic semilinear equations arising in population dynamics, either in finite time or infinite time. These are the monostable and bistable equations on $(0,L)$ for a density of individuals $0 \leq…

Optimization and Control · Mathematics 2019-02-20 Camille Pouchol , Emmanuel Trélat , Enrique Zuazua

We study the boundary control problems for the wave, heat, and Schr\"odinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting…

Optimization and Control · Mathematics 2025-05-28 S. A. Avdonin , V. S. Mikhaylov

We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…

Analysis of PDEs · Mathematics 2017-12-29 Dorota Bors

A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…

Optimization and Control · Mathematics 2017-09-07 Robert Vrabel

This paper establishes the local exact controllability of the quasilinear porous media equation with Dirichlet boundary condition.\\ Consider the equation $$\begin{aligned} &y_t - \Delta a(y) = mu+f \text{ on } Q\\ &y(0)=y_0,\ y…

Analysis of PDEs · Mathematics 2024-06-25 Marius Beceanu

In this paper, we consider a nonlinear system of two parabolic equations, with a distributed control in the first equation and an odd coupling term in the second one. We prove that the nonlinear system is small-time locally…

Analysis of PDEs · Mathematics 2022-12-16 Kévin Le Balc'h , Takéo Takahashi

We investigate a nonstandard phase field model of Cahn-Hilliard type. The model describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in the papers…

Analysis of PDEs · Mathematics 2012-01-31 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In this paper we study the boundary controllability for a system of two coupled degenerate/singular parabolic equations with a control acting on only one equation. We analyze both approximate and null boundary controllability properties.…

Optimization and Control · Mathematics 2021-04-02 Brahim Allal , Abdelkarim Hajjaj , Jawad Salhi , Amine Sbai

We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop…

Optimization and Control · Mathematics 2022-03-09 Marc Puche , Timo Reis , Felix Schwenninger

We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…

Mathematical Physics · Physics 2007-05-23 David Hasler , Jan Philip Solovej

This work represents a first contribution on the problem of boundary stabilization for the phase field system of Cahn-Hilliard type, which models the phase separation in a binary mixture. The feedback controller we design here is with…

Analysis of PDEs · Mathematics 2018-12-03 Pierluigi Colli , Gianni Gilardi , Ionut Munteanu

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…

Optimization and Control · Mathematics 2014-01-23 Denys Khusainov , Michael Pokojovy , Elvin Azizbayov

In this paper we consider the one-phase Stefan problem with surface tension, set in a two-dimensional strip-like geometry, with periodic boundary conditions respect to the horizontal direction $x_1\in\mathbb{T}$. We prove that the system is…

Optimization and Control · Mathematics 2022-09-09 Borjan Geshkovski , Debayan Maity

This paper proposes a novel control framework for handling (potentially coupled) multiple time-varying output constraints for uncertain nonlinear systems. First, it is shown that the satisfaction of multiple output constraints boils down to…

Systems and Control · Electrical Eng. & Systems 2025-01-08 Farhad Mehdifar , Lars Lindemann , Charalampos P. Bechlioulis , Dimos V. Dimarogonas