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We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…

Probability · Mathematics 2023-01-10 Joe Jackson , Daniel Lacker

While the use of combination therapy is increasing in prevalence for cancer treatment, it is often difficult to predict the exact interactions between different treatment forms, and their synergistic/antagonistic effects on patient health…

Optimization and Control · Mathematics 2021-01-29 Jayanth Pratap

We introduce the problem of parameter identification for a coupled nonlocal Cahn-Hilliard-reaction-diffusion PDE system stemming from a recently introduced tumor growth model. The inverse problem of identifying relevant parameters is…

Analysis of PDEs · Mathematics 2020-09-24 Elisabetta Rocca , Luca Scarpa , Andrea Signori

This paper analyzes a discretization of a stochastic parabolic optimal control problem, where the diffusion term contains the control variable. With rough data, the convergence of the discretization is derived. In addition, a Monte-Carlo…

Numerical Analysis · Mathematics 2022-08-31 Binjie Li , Qin Zhou , Xiaoping Xie

A phase field model for tumour growth is introduced that is based on a Brinkman law for convective velocity fields. The model couples a convective Cahn-Hilliard equation for the evolution of the tumour to a reaction-diffusion-advection…

Analysis of PDEs · Mathematics 2021-09-07 Matthias Ebenbeck , Harald Garcke , Robert Nürnberg

This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and…

Probability · Mathematics 2007-05-23 Vivek S. Borkar

In their recent work `Well-posedness, regularity and asymptotic analyses for a fractional phase field system' (Asymptot. Anal. 114 (2019), 93-128; see also the preprint arXiv:1806.04625), two of the present authors have studied phase field…

Analysis of PDEs · Mathematics 2020-05-28 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

A macroscopic model of the tumor Gompertzian growth is proposed. This approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor factors.…

Tissues and Organs · Quantitative Biology 2017-08-23 Paolo Castorina , Dario Zappalá

It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression…

Biological Physics · Physics 2024-12-05 Nonthakorn Olaranont , Chaozhen Wei , John Lowengrub , Min Wu

A macroscopic model of the tumor Gompertzian growth is proposed. The new approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor…

Cell Behavior · Quantitative Biology 2007-05-23 Paolo Castorina , Dario Zappala'

This paper is to investigate the control problem of maximizing the net benefit of a single species while the cost of the resource allocation is minimized in a population model which can be described by a reaction diffusion advection…

Optimization and Control · Mathematics 2019-01-01 Lianzhang Bao , Huilai Li , Haojian Liang , Guangliang Zhao

We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…

Numerical Analysis · Mathematics 2025-10-23 Agus L. Soenjaya , Ping Lin , Thanh Tran

This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are…

Optimization and Control · Mathematics 2025-11-03 Nicolas Hoischen , Petar Bevanda , Stefan Sosnowski , Sandra Hirche , Boris Houska

Cancer is a disease driven by random DNA mutations and the interaction of many complex phenomena. To improve the understanding and ultimately find more effective treatments, researchers leverage computer simulations mimicking the tumor…

Computational Physics · Physics 2024-01-26 Tobias Duswald , Ernesto A. B. F. Lima , J. Tinsley Oden , Barbara Wohlmuth

Optimal control of nonlinear acoustic waves is relevant in many medical ultrasound technologies, ranging from cancer therapy to targeted drug delivery, where it can help guide the precise deposition of acoustic energy. In this work, we…

Optimization and Control · Mathematics 2025-11-20 Vanja Nikolić , Belkacem Said-Houari

In this paper we propose two nonlinear models for the control of anthracnose disease. The first is an ordinary differential equation (ODE) model which represents the within-host evolution of the disease. The second includes spatial…

Optimization and Control · Mathematics 2014-06-17 David Fotsa , Elvis Houpa , David Békollé , Christopher Thron , Michel Ndoumbé

In this work, we study the control constrained distributed optimal control of a stationary doubly diffusive flow model. For the control problem, we use a well-posedness analysis based on minimal assumptions on data and domain. We show the…

Optimization and Control · Mathematics 2025-06-13 Jai Tushar , Arbaz Khan , Manil T. Mohan

An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…

Dynamical Systems · Mathematics 2019-10-30 Yuri Kozitsky

We introduce a nonisothermal phase-field system of Caginalp type that describes tumor growth under hyperthermia. The model couples a possibly viscous Cahn-Hilliard equation, governing the evolution of the healthy and tumor phases, with an…

Analysis of PDEs · Mathematics 2025-10-13 Giulia Cavalleri , Pierluigi Colli , Elisabetta Rocca

This paper is about numerical control of HIV propagation. The contribution of the paper is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the…

Systems and Control · Computer Science 2023-05-30 Dmitry Gromov , Ingo Bulla , Ethan O. Romero-Severson , Oana Silvia Serea