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Related papers: On a Class of Boundary Control Problems

200 papers

This paper is devoted to the partial null controllability issue of parabolic linear systems with n equations. Given a bounded domain in R N, we study the effect of m localized controls in a nonempty open subset only controlling p components…

Analysis of PDEs · Mathematics 2017-01-20 Farid Ammar Khodja , Franz Chouly , Michel Duprez

We consider an elliptic problem with unknowns on the boundary of the domain of the elliptic equation and suppose that the right-hand side of this equation is square integrable and that the boundary data are arbitrary (specifically,…

Analysis of PDEs · Mathematics 2020-07-28 Iryna Chepurukhina , Aleksandr Murach

We examine various density results related to the solutions of the non-local heat equation at a specific time slice, focusing on two distinct models: one with homogeneous Dirichlet boundary condition and the other with singular boundary…

Analysis of PDEs · Mathematics 2025-12-30 Saumyajit Das

In this paper we study the existence of sufficiently regular representations of Hamilton-Jacobi equations in the optimal control theory with unbounded control set. We use a new method to construct representations for a wide class of…

Optimization and Control · Mathematics 2021-08-17 Arkadiusz Misztela

We study (approximate) null-controllability of parabolic equations in $L_p(\mathbb{R}^d)$ and provide explicit bounds on the control cost. In particular we consider systems of the form $\dot{x}(t) = -A_p x(t) + \mathbf{1}_E u(t)$, $x(0) =…

Functional Analysis · Mathematics 2022-10-31 Clemens Bombach , Dennis Gallaun , Christian Seifert , Martin Tautenhahn

Stabilization of partial differential equations is a topic of utmost importance in mathematics as well as in engineering sciences. Concerning one dimensional problems there exists a well developed theory. Due to numerous important…

Optimization and Control · Mathematics 2025-01-24 Michael Herty , Ferdinand Thein

This technical note is concerned with boundary stabilization of multi-dimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive…

Optimization and Control · Mathematics 2025-02-24 Haitian Yang , Wen-An Yong

We consider elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space $W$. The system is equipped with a general class of coupled boundary…

Analysis of PDEs · Mathematics 2018-12-21 Stefano Cardanobile , Delio Mugnolo

In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a…

Analysis of PDEs · Mathematics 2013-11-13 Matthieu Felsinger , Moritz Kassmann , Paul Voigt

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

Optimization and Control · Mathematics 2022-10-03 Harbir Antil , Hugo Díaz

This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions.…

Analysis of PDEs · Mathematics 2007-05-23 F. Ancona , A. Bressan , G. M. Coclite

For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property is equivalent to exact null controllability. We…

Optimization and Control · Mathematics 2017-10-24 Rabah Rabah , Grigory Sklyar , Pavel Yu. Barkhayev , Pavel Barkhayev , Grzegorz Szkibiel

We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the…

Analysis of PDEs · Mathematics 2023-11-16 Igor Kukavica , Šárka Nečasová , Amjad Tuffaha

We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved…

Optimization and Control · Mathematics 2022-03-18 Timm Strecker , Ole Morten Aamo , Michael Cantoni

This paper completely solves the controllability problems of two-dimensional multi-input discrete-time bilinear systems with and without drift. Necessary and sufficient conditions for controllability, which cover the existing results, are…

Systems and Control · Computer Science 2014-01-23 Lin Tie

This paper presents bilateral control laws for one-dimensional(1-D) linear 2x2 hyperbolic first-order systems (with spatially varying coefficients). Bilateral control means there are two actuators at each end of the domain. This situation…

Optimization and Control · Mathematics 2024-09-04 Wei Sun , Jing Li , Liangyu Xu

In this article we address the issue of uniqueness for differential and algebraic operator Riccati equations, under a distinctive set of assumptions on their unbounded coefficients. The class of boundary control systems characterized by…

Optimization and Control · Mathematics 2021-02-02 Paolo Acquistapace , Francesca Bucci

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…

Probability · Mathematics 2016-12-05 Giuseppina Guatteri

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

Optimization and Control · Mathematics 2024-04-04 Christoph Buchheim , Alexandra Grütering , Christian Meyer

We consider optimal control problems of systems governed by stationary, incompressible generalized Navier-Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of…

Optimization and Control · Mathematics 2015-10-15 Telma Guerra , Jorge Tiago , Adélia Sequeira