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This work is concerned with the possibility of proving the boundary null controllability for the degenerate wave equation, developing the asymptotic analysis of a suitable family of state-control pairs $((u_\varepsilon ,…

Optimization and Control · Mathematics 2023-11-15 Bruno S. V. Araújo , Reginaldo Demarque , Luiz Viana

In this paper we deal with the controllability problem for some Sobolev type equations. We show that the equations cannot be driven to zero if the control region is strictly supported within the domain. Nevertheless, we also prove that it…

Analysis of PDEs · Mathematics 2024-02-02 F. W. Chaves-Silva , Diego A. Souza

We consider linear one-dimensional parabolic equations with space dependent coefficients that are only measurable and that may be degenerate or singular.Considering generalized Robin-Neumann boundary conditions at both extremities, we prove…

Analysis of PDEs · Mathematics 2015-09-03 Philippe Martin , Lionel Rosier , Pierre Rouchon

This paper deals with the null controllability of a coupled parabolic system, which is Kuramoto-Sivashinsky-Korteweg-de Vries equation coupled with heat equation through first order derivative. More precisely, we prove the null…

Analysis of PDEs · Mathematics 2022-05-20 Manish Kumar , Subrata Majumdar

This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain of R^N (N>1) with coupling terms of zero and first orders and one control localized in some…

Analysis of PDEs · Mathematics 2020-04-02 Michel Duprez , Pierre Lissy

We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…

Numerical Analysis · Mathematics 2023-06-13 Erik Burman , Ali Feizmohammadi , Arnaud Munch , Lauri Oksanen

In this paper we prove an exact controllability result for the Vlasov-Stokes system in the two-dimensional torus with small data by means of an internal control. We show that one can steer, in arbitrarily small time, any initial datum of…

Analysis of PDEs · Mathematics 2016-01-13 Iván Moyano

We prove controllability of the Schr\"odinger equation in $\mathbb{R}^d$ in any time $T > 0$ with internal control supported on nonempty, periodic, open sets. This demonstrates in particular that controllability of the Schr\"odinger…

Analysis of PDEs · Mathematics 2023-03-13 Matthias Täufer

In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the…

Analysis of PDEs · Mathematics 2021-01-25 Stéphane Gerbi , Chiraz Kassem , Amina Mortada , Ali Wehbe

In this paper we treat controllability properties for the linear Kuramoto-Sivashinsky equation on a network with two types of boundary conditions. More precisely, the equation is considered on a star-shaped tree with Dirichlet and Neumann…

Optimization and Control · Mathematics 2018-06-15 Cristian M. Cazacu , Liviu I. Ignat , Ademir F. Pazoto

This paper is devoted to the study of the approximate controllability for a one-dimensional wave equation in domains with moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving.…

Optimization and Control · Mathematics 2025-01-14 Isaías Pereira de Jesus

In this paper, we study the controllability of the two-dimensional relativistic Vlasov-Maxwell system in a torus, by means of an interior control. We give two types of results. With the geometric control condition on the control set, we…

Analysis of PDEs · Mathematics 2012-12-03 Olivier Glass , Daniel Han-Kwan

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…

Optimization and Control · Mathematics 2019-01-16 Mohamed Ouzahra

This paper studies the memory-type null controllability of a class of one-dimensional non-autonomous degenerate parabolic equations with Volterra-type memory terms. The diffusion operator is considered in both divergence and non-divergence…

Optimization and Control · Mathematics 2026-04-06 Dev Prakash Jha , Raju K. George

We consider the null-controllability problem for the generalized Baouendi-Grushin equation $(\partial_t - \partial_x^2 - q(x)^2\partial_y^2)f = 1_\omega u$ on a rectangular domain. Sharp controllability results already exist when the…

Optimization and Control · Mathematics 2022-07-08 Jérémi Dardé , Armand Koenig , Julien Royer

Our goal is to study controllability and observability properties of the 1D heat equation with internal control (or observation) set $\omega_{\varepsilon}=(x_{0}-\varepsilon, x_{0}+\varepsilon )$, in the limit $\varepsilon\rightarrow 0$,…

Analysis of PDEs · Mathematics 2020-02-07 Cyril Letrouit

This article is devoted to study the interior approximated controllability of the strongly damped semilinear wave equation with memory, impulses and delay terms. The problem is challenging since the state equation contains memory and…

Optimization and Control · Mathematics 2017-04-11 Cristi Guevara , Hugo Leiva

This paper deals with the controllability for a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. This equation models small vibrations of a string where an endpoint is fixed and the other is moving.…

Analysis of PDEs · Mathematics 2025-02-03 Isaías Pereira de Jesus

We investigate the null controllability property of the parabolic equation associated with the Grushin operator defined by the canonical almost-Riemannian structure on the 2-dimensional sphere $\mathbb S^2$. This is the natural…

Optimization and Control · Mathematics 2022-05-17 Cyprien Tamekue

In this work, we investigate the small-time global controllability properties of a class of fourth-order nonlinear parabolic equations driven by a bilinear control posed on the one-dimensional torus. The controls depend only on time and act…

Optimization and Control · Mathematics 2026-01-13 Subrata Majumdar , Debanjit Mondal