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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

The aim of this work is to present some strategies to solve numerically controllability problems for the two-dimensional heat equation, the Stokes equations and the Navier-Stokes equations with Dirichlet boundary conditions. The main idea…

Optimization and Control · Mathematics 2024-02-12 Enrique Fernández-Cara , Arnaud Münch , Diego A. Souza

The goal of this paper is to analyze control properties of the parabolic equation with variable coefficients in the principal part and with a singular inverse-square potential:\,$\partial_tu(x,t)-{\rm div}(p(x)\nabla…

Analysis of PDEs · Mathematics 2018-11-15 Xue Qin , Shumin Li

In this paper, we discuss the approximate controllability for control systems governed by stochastic evolution hemivariational inequalities in Hilbert spaces. The interest in studying this type of equation comes from its application in some…

Optimization and Control · Mathematics 2025-04-22 Bholanath Kumbhakar , Deeksha , Dwijendra Narain Pandey

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a…

Probability · Mathematics 2015-05-13 S. Bonaccorsi , F. Confortola , E. Mastrogiacomo

We establish boundary observability and control for the fractional heat equation over arbitrary time horizons $T > 0$, within the optimal range of fractional exponents $s \in (1/2, 1)$. Our approach introduces a novel synthesis of…

Analysis of PDEs · Mathematics 2025-04-25 Umberto Biccari , Mahamadi Warma , Enrique Zuazua

We consider the heat equation with dynamic bounary conditions involving gradient terms in a bounded domain. In this paper we study the cost of approximate controllability for this equation. Combining new developed Carleman estimates and…

Analysis of PDEs · Mathematics 2022-01-04 I. Boutaayamou , S. E. Chorfi , L. Maniar , O. Oukdach

This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…

Optimization and Control · Mathematics 2024-09-17 S. E. Chorfi , L. Maniar

In this paper, we study the long-time behavior of a stochastic heat equation with multiplicative noise and localized control. We begin by analyzing the uncontrolled dynamics and derive explicit decay rates for both mean-square and almost…

Optimization and Control · Mathematics 2026-04-13 Víctor Hernández-Santamaría , Kévin Le Balc'h , Liliana Peralta

In this paper we study the optimality condition for the Venttsel boundary control of a parabolic equation, that is, the state of the dynamic system is governed by a parabolic equation together with an initial condition while the control is…

Analysis of PDEs · Mathematics 2014-11-10 Yousong Luo

In this paper, we investigate the existence and uniqueness of solutions for a class of evolutionary integral equations perturbed by a noise arising in the theory of heat conduction. As a motivation of our results, we study an optimal…

Optimization and Control · Mathematics 2011-12-06 F. Cconfortola , E. Mastrogiacomo

We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…

Analysis of PDEs · Mathematics 2020-03-03 Ugur G. Abdulla , Evan Cosgrove

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 investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…

Optimization and Control · Mathematics 2026-01-27 Zengyu Li , Qi Lü , Yu Wang , Haitian Yang

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 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

We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…

Optimization and Control · Mathematics 2018-09-05 Peter Benner , Christoph Trautwein

In this paper, we consider forward stochastic nonlinear parabolic equations, with a control localized in the drift term. Under suitable assumptions, we prove the small-time global null-controllability, with a truncated nonlinearity. We also…

Analysis of PDEs · Mathematics 2020-09-28 Victor Hernandez-Santamaria , Kevin Le Balc'h , Liliana Peralta

This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for…

Optimization and Control · Mathematics 2025-08-19 Christian Bayer , Boualem Djehiche , Eliza Rezvanova , Raul Fidel Tempone

We study the null controllability for a degenerate/singular wave equation with drift in non divergence form. In particular, considering a control localized on the non degenerate boundary point, we provide some conditions for the boundary…

Analysis of PDEs · Mathematics 2024-07-10 Genni Fragnelli , Dimitri Mugnai , Amine Sbai