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In the present work we investigate an optimal control problem related to the following chemotaxis-consumption model in a bounded domain $\Omega\subset \mathbb{R}^3$: $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla v), \quad \partial_t…

Optimization and Control · Mathematics 2024-02-12 Francisco Guillén-González , André Luiz Corrêa Vianna Filho

We consider a system of two coupled integro-differential equations modelling populations of healthy and cancer cells under therapy. Both populations are structured by a phenotypic variable, representing their level of resistance to the…

Optimization and Control · Mathematics 2016-12-15 Camille Pouchol , Jean Clairambault , Alexander Lorz , Emmanuel Trélat

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

Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory…

Optimization and Control · Mathematics 2017-04-20 Ouassim Bara , Seddik Djouadi , Judy Day , Suzanne Lenhart

We provide an overview of an optimal control problem within a stochastic model of tumor growth, which includes drug application. The model comprises two stochastic differential equations (SDE) representing the diffusion of nutrient and drug…

Optimization and Control · Mathematics 2024-11-12 Noelymar Farinacci

A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…

Optimization and Control · Mathematics 2022-11-24 Bui Trong Kien , Bui Ngoc Muoi , Ching-Feng Wen , Jen-Chih Yao

We study the problem of controlling the initial condition of a vibrating beam. The optimal control problem seeks to determine solutions of initial velocity that assure the approach of the state of the beam to a given target function in the…

Optimization and Control · Mathematics 2025-02-10 Yesim Akbulut , Bismark Singh

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

Optimization and Control · Mathematics 2015-03-19 Morten Vierling

In this paper, we study an optimal control problem for a macroscopic mechanical tumour model based on the phase field approach. The model couples a Cahn--Hilliard type equation to a system of linear elasticity and a reaction-diffusion…

Optimization and Control · Mathematics 2021-04-21 Harald Garcke , Kei Fong Lam , Andrea Signori

We investigate several control strategies for the transport of an excitation along a spin chain. We demonstrate that fast, high fidelity transport can be achieved using protocols designed with differentiable programming. Building on this,…

Quantum Physics · Physics 2022-11-30 Luuk Coopmans , Steve Campbell , Gabriele De Chiara , Anthony Kiely

In this paper we study a bilinear optimal control problem associated to a chemo-repulsion model with linear production term. We analyze the existence, uniqueness and regularity of pointwise strong solutions in a bidimensional domain. We…

Optimization and Control · Mathematics 2019-01-23 Francisco Guillén González , Exequiel Mallea-Zepeda , María Ángeles Rodríguez-Bellido

This paper treats a distributed optimal control problem for a tumor growth model of Cahn-Hilliard type including chemotaxis. The evolution of the tumor fraction is governed by a variational inequality corresponding to a double obstacle…

Optimization and Control · Mathematics 2021-04-21 Pierluigi Colli , Andrea Signori , Jürgen Sprekels

The interactions between tumor cells and the immune system play a crucial role in cancer evolution. In this study, we explore how these interactions influence cancer progression by modeling the relationships among naive T cells, effector T…

Tissues and Organs · Quantitative Biology 2025-03-19 Haifeng Zhang , Changjing Zhuge , Jinzhi Lei

We are concerned about the controllability of a general linear hyperbolic system of the form $\partial_t w (t, x) = \Sigma(x) \partial_x w (t, x) + \gamma C(x) w(t, x) $ ($\gamma \in \mR$) in one space dimension using boundary controls on…

Optimization and Control · Mathematics 2018-12-05 Jean-Michel Coron , Hoai-Minh Nguyen

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case, such as: given a fixed interaction between the system…

Quantum Physics · Physics 2009-11-10 H. M . Wiseman , A. C. Doherty

In this paper, we consider the problem of controlling a diffusion process pertaining to an opioid epidemic dynamical model with random perturbation so as to prevent it from leaving a given bounded open domain. Here, we assume that the…

Optimization and Control · Mathematics 2018-06-26 Getachew K. Befekadu , Quanyan Zhu

This paper is intended to tackle the control problem associated with an extended phase field system of Cahn-Hilliard type that is related to a tumor growth model. This system has been investigated in previous contributions from the…

Analysis of PDEs · Mathematics 2018-11-26 Andrea Signori

Control problem in a biological system is the problem of finding an interventional policy for changing the state of the biological system from an undesirable state, e.g. disease, into a desirable healthy state. Boolean networks are utilized…

Molecular Networks · Quantitative Biology 2016-09-07 Mohammad Moradi , Sama Goliaei

The KWC system is a well-known generic framework for phase-field models of grain boundary motion, whose original formulation is given as a parabolic gradient flow of a free energy. In the original KWC system, the results of uniqueness have…

Optimization and Control · Mathematics 2025-06-12 Harbir Antil , Daiki Mizuno , Ken Shirakawa

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