Related papers: Optimal treatment planning governed by kinetic equ…
The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…
The paper considers a linear system of Boltzmann transport equations modelling the evolution of three species of particles, photons, electrons and positrons. The system is coupled because of the collision term (an integral operator). The…
We study the problem of finding an optimal radiotherapy treatment plan. A time-dependent Boltzmann particle transport model is used to model the interaction between radiative particles with tissue. This model allows for the modeling of…
This work develops a rigorous mathematical formulation of proton transport by integrating both deterministic and stochastic perspectives. The deterministic framework is based on the Boltzmann-Fokker-Planck equation, formulated as an…
An optimal control problem in the space of Borel measures governed by the Poisson equation is investigated. The characteristic feature of the problem under consideration is the Tikhonov regularization term in form of the transportation…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
We extend the Boltzmann-Hamel equations to the optimal control setting, producing a set of equations for both kinematic and dynamic nonholonomic optimal control problems. In particular, we will show the dynamic optimal control problem can…
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…
This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
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…
We consider image registration as an optimal control problem using an optical flow formulation, i.e., we discuss an optimization problem that is governed by a linear hyperbolic transport equation. Requiring Lipschitz continuity of the…
In this paper, we study a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase field variable coupled to a reaction diffusion equation for the…
In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under constraints. For this problem a…
We study treatment assignment problems under capacity constraints, where a planner aims to maximize social welfare by assigning treatments based on observable covariates. Such constraints, common when treatments are costly or limited in…
In this study, we describe a procedure of topology optimization in the framework of the linear Boltzmann equation, implemented using a reference Monte-Carlo particle transport code. This procedure can design complex structures that optimize…
Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets.…
Radiative transfer in curved spacetimes has become increasingly important to understanding high-energy astrophysical phenomena and testing general relativity in the strong field limit. The equations of radiative transfer are physically…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents…