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In this paper, we study the following parabolic chemo-repulsion with nonlinear production model: $$ \left\{ \begin{array}{rcl} \partial_tu-\Delta u&=&\nabla\cdot(u\nabla v),\\ \partial_tv-\Delta v+v&=&u^p+fv\, 1_{\Omega_c}. \end{array}…

Analysis of PDEs · Mathematics 2020-02-17 Francisco Guillén-González , Exequiel Mallea-Zepeda , Élder J. Villamizar-Roa

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

In this paper, we discuss the distributed control problem governed by the following parabolic integro-differential equation (PIDE) in the abstract form \begin{eqnarray*} \frac{\partial y}{\partial t} + A y &=& \int_0^t B(t, s) y(s) ds + Gu,…

Optimization and Control · Mathematics 2016-06-14 Anil Kumar , Amiya K. Pani , Mohan C. Joshi

We discuss the problem of optimal impulse control representing the preventive maintenance of a simple reparable system. The system model is governed by coupled transport and integro-differential equations in a nonreflexive Banach space. The…

Optimization and Control · Mathematics 2017-03-29 Weiwei Hu , Rongjie Lai , Houbao Xu , Chuang Zheng

This project investigates the approximate controllability of a class of stochastic integrodifferential equations in Hilbert space with non-local beginning conditions. In a departure from the conventional concerns expressed in the…

Optimization and Control · Mathematics 2026-02-10 Mamadou Pathe LY , Ravikumar Kasinathan , Ramkumar Kasinathan , Dimplekumar Chalishajar , Mamadou Abdoul Diop

This paper extends our previous controllability results for a class of coupled linear parabolic systems with nonlocal interactions, motivated by applications in finance such as generalized Black--Scholes models. We establish local null…

Analysis of PDEs · Mathematics 2025-12-02 Juan Limaco , Rafael Martins Lobosco , Luis P. Yapu

In this paper, we investigate the controllability of bilinear control systems of the form $\dot{s} = As + uBs$, where $s \in \mathbb{S}^2$ and $A, B \in gl(3, \mathbb{R})$ are skew-symmetric matrices. First, we prove that the algebraic…

Optimization and Control · Mathematics 2025-06-10 Marco A. Colque-Choquecallata , Efrain Cruz-Mullisaca , Victor H. Patty-Yujra

This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form $\|u(t)\|_{L^1(\Omega)} \le \gamma$ for $t \in (0,T)$. This limits the total control that can be…

Optimization and Control · Mathematics 2021-12-03 Eduardo Casas , Karl Kunisch

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

We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on controllability results through Carleman estimates for the associated adjoint problem. The novelty of the present paper is that the…

Analysis of PDEs · Mathematics 2014-02-10 Genni Fragnelli , Dimitri Mugnai

In this article we study a controllability problem for a parabolic and a hyperbolic partial differential equations in which the control is the shape of the domain where the equation holds. The quantity to be controlled is the trace of the…

Analysis of PDEs · Mathematics 2012-11-07 Jonathan Touboul

In this paper we study the null controllability of some non diagonalizable degenerate parabolic systems of PDEs, we assume that the diffusion, coupling and controls matrices are constant and we characterize the null controllability by an…

Optimization and Control · Mathematics 2018-08-24 E. M. Ait Ben Hassi , M. Fadili , L. Maniar

In this paper, we apply the hierarchical strategy to a semilinear weakly degenerate parabolic equation involving a gradient term. We use the Stackelberg-Nash strategy with one leader which tries to drive the solution to zero and two…

Optimization and Control · Mathematics 2022-09-27 Landry Djomegne , Cyrille Kenne , René Dorville , Pascal Zongo

This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss the approximate controllability of…

Optimization and Control · Mathematics 2022-01-03 Sumit Arora , Soniya Singh , Manil T. Mohan , Jaydev Dabas

This paper deals with the null-controllability of a system of {\em mixed parabolic-elliptic pdes} at any given time $T>0$. More precisely, we consider the \textit{Kuramoto-Sivashinsky--Korteweg-de Vries equation} coupled with a second order…

Analysis of PDEs · Mathematics 2025-05-29 Kuntal Bhandari , Subrata Majumdar

This paper is addressed to a study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish a key weighted identity for partial differential operators…

Optimization and Control · Mathematics 2008-05-27 Xiaoyu Fu

In this paper we prove that the Ball-Marsden-Slemrod controllability obstruction also holds for nonlinear equations, with integrable bilinear controls. We first show an abstract result and then we apply it to nonlinear wave equations. The…

Optimization and Control · Mathematics 2019-05-03 Thomas Chambrion , Laurent Thomann

In this paper we present a null controllability result for a degenerate semilinear parabolic equation with first order terms. The main result is obtained after the proof of a new Carleman inequality for a degenerate linear parabolic…

Optimization and Control · Mathematics 2019-07-09 J. Carmelo Flores , Luz de Teresa

The main purpose of this paper is to show the global stabilization and exact controllability properties for a fourth order nonlinear fourth order nonlinear Schr\"odinger system: $$i\partial_tu +\partial_x^2u-\partial_x^4u=\lambda |u|^2u,$$…

Analysis of PDEs · Mathematics 2021-07-26 Roberto Capistrano Filho , Márcio Cavalcante

This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…

Optimization and Control · Mathematics 2018-04-30 Christian Clason , Armin Rund , Karl Kunisch