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We propose and analyze an optimal control problem associated with a Keller-Segel type parabolic system with chemoattraction, modeling the glioblastoma growth in a bi-dimensional bounded domain, influenced by the presence of oxygen where the…

Optimization and Control · Mathematics 2026-04-24 Juan J. Forero-Hernańdez , Francisco Guillén-González , Élder J. Villamizar-Roa

The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and…

Numerical Analysis · Mathematics 2023-10-04 Daniel Acosta-Soba , Francisco Guillén-González , J. Rafael Rodríguez-Galván

As a class of nonlinear partial differential equations, the Keller-Segel system is widely used to model chemotaxis in biology. In this paper, we present the construction and analysis of a decoupled linear, mass-conservative, block-centered…

Numerical Analysis · Mathematics 2025-01-24 Jie Xu , Hongfei Fu

This paper aims to develop numerical approximations of the Keller--Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or…

Numerical Analysis · Mathematics 2022-07-25 Santiago Badia , Jesús Bonilla , Juan Vicente Gutiérrez-Santacreu

An optimal control problem associated to the Keller-Segel with logistic reaction system will be studied in $2D$ domains. The control acts in a bilinear form only in the chemical equation. The existence of optimal control and a necessary…

Optimization and Control · Mathematics 2022-07-01 P. Braz e Silva , F. Guillén-González , C. F. Perusato , M. A. Rodríguez-Bellido

In this paper, we consider the fast numerical solution of an optimal control formulation of the Keller--Segel model for bacterial chemotaxis. Upon discretization, this problem requires the solution of huge-scale saddle point systems to…

Numerical Analysis · Mathematics 2018-06-25 Sergey Dolgov , John W. Pearson

Keller-Segel systems are a set of nonlinear partial differential equations used to model chemotaxis in biology. In this paper, we propose two alternating direction implicit (ADI) schemes to solve the 2D Keller-Segel systems directly with…

Numerical Analysis · Mathematics 2026-02-11 Yubin Lu , Chi-An Chen , Xiaofan Li , Chun Liu

This paper considers the optimal boundary control of chemical systems described by advection-diffusion-reaction (ADR) equations. We use a discontinuous Galerkin finite element method (DG-FEM) for the spatial discretization of the governing…

Numerical Analysis · Mathematics 2024-11-27 Marcus Johan Schytt , John Bagterp Jørgensen

In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…

Numerical Analysis · Mathematics 2018-10-09 Jerome Droniou , Neela Nataraj , Devika Shylaja

This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior…

Optimization and Control · Mathematics 2025-03-21 Chuanzhi Lv , Hongdan Li , Huanshui Zhang

For a Keller-Segel model for chemotaxis in two spatial dimensions we consider a modification of a positivity preserving fully discrete scheme using a local extremum diminishing flux limiter. We discretize space using piecewise linear finite…

Numerical Analysis · Mathematics 2026-02-20 Panagiotis Chatzipantelidis , Christos Pervolianakis

The paper that follows describes a numerical algorithm to solve the parabolic-parabolic Keller--Segel system characterized by singular sensitivity and signal absorption in such a manner that the numerical approximations converge towards a…

Numerical Analysis · Mathematics 2026-04-01 Juan Vicente Gutiérrez-Santacreu

In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…

Optimization and Control · Mathematics 2023-06-23 Gabriel Velho , Jean Auriol , Riccardo Bonalli

We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…

Optimization and Control · Mathematics 2021-10-08 Qinsheng Zhang , Amirhossein Taghvaei , Yongxin Chen

We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…

Optimization and Control · Mathematics 2021-02-01 Simone Göttlich , Claudia Totzeck

This paper considers the optimal control problem for realizing logical gates in a closed quantum system. The quantum state is governed by Schrodinger's equation, which we formulate as a time-dependent Hamiltonian system in terms of the real…

We consider the Keller-Segel model of chemotaxis on one-dimensional networks. Using a variational characterization of solutions, positivity preservation, conservation of mass, and energy estimates, we establish global existence of weak…

Numerical Analysis · Mathematics 2018-05-03 Herbert Egger , Lucas Schöbel-Kröhn

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

Optimization and Control · Mathematics 2019-07-26 Sebastian Engel , Philip Trautmann , Boris Vexler

We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…

Analysis of PDEs · Mathematics 2024-12-12 Abhishek Chaudhary

We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…

Optimization and Control · Mathematics 2026-04-21 Jochen Schmid , Philipp Seufert , Jan Schwientek , Tobias Seidel , Karl-Heinz Küfer
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