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We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…

Tissues and Organs · Quantitative Biology 2020-06-02 Chiara Villa , Mark A. J. Chaplain , Tommaso Lorenzi

We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003,…

Analysis of PDEs · Mathematics 2020-06-24 Andrea Genovese de Oliveira , John R. King

In this paper, a free boundary problem modelling the growth of tumor is considered. The model includes two reaction-diffusion equations modelling the diffusion of nutrient and drug in the tumor and three hyperbolic equations describing the…

Numerical Analysis · Mathematics 2020-01-29 Sakine Esmaili , F. Nasresfahani , M. R. Eslahchi

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

Analysis of PDEs · Mathematics 2016-11-01 Ugur G. Abdulla

We introduce a new phase field model for tumour growth where viscoelastic effects are taken into account. The model is derived from basic thermodynamical principles and consists of a convected Cahn--Hilliard equation with source terms for…

Numerical Analysis · Mathematics 2024-06-21 Harald Garcke , Balázs Kovács , Dennis Trautwein

In cancer research, the role of the extracellular matrix (ECM) and its associated matrix-degrading enzyme (MDE) has been a significant area of focus. This study presents a numerical algorithm designed to simulate a previously established…

Numerical Analysis · Mathematics 2025-03-25 Qiumei Huang , Zhonghua Qiao , Cheng Wang , Huiting Yang

Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…

Optimization and Control · Mathematics 2024-03-12 Qin Li , Li Wang , Yunan Yang

Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…

Optimization and Control · Mathematics 2024-10-10 Houra Mahmoudzadeh , Kimia Ghobadi

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

In this work, we analyze a diffuse-interface model for tumor growth, subject to multiplicative white noises, posed on a bounded domain $\mathcal{O} \subset \mathbb{R}^d$, $d=2,3$. The model couples a stochastic incompressible convective…

Analysis of PDEs · Mathematics 2026-05-29 Kalpana Rawat , Kumarasamy Sakthivel

High-fidelity operation of quantum computers requires precise knowledge of the physical system through characterization. For motion-mediated entanglement generation in trapped ions, it is crucial to have precise knowledge of the…

Quantum Physics · Physics 2024-04-22 Qiyao Liang , Mingyu Kang , Ming Li , Yunseong Nam

This paper is concerned with a phase field system of Cahn-Hilliard type that is related to a tumor growth model and consists of three equations in terms of the variables order parameter, chemical potential and nutrient concentration. This…

Analysis of PDEs · Mathematics 2015-03-04 Pierluigi Colli , Gianni Gilardi , Elisabetta Rocca , Jürgen Sprekels

Tumor-immune interactions are central to cancer progression and treatment outcomes. In this study, we present a stochastic agent-based model that integrates cellular heterogeneity, spatial cell-cell interactions, and drug resistance…

Tissues and Organs · Quantitative Biology 2026-05-19 Yuhong Zhang , Chenghang Li , Boya Wang , Jinzhi Lei

In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…

Optimization and Control · Mathematics 2023-11-27 Stephan Dempe , Markus Friedemann , Felix Harder , Patrick Mehlitz , Gerd Wachsmuth

In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…

Dynamical Systems · Mathematics 2023-03-21 Marvin Fritz

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…

Mathematical Physics · Physics 2017-01-20 Andrea Tosin

We consider a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects which is introduced in [2]. It is comprised of phase-field equation to describe tumor growth, which is coupled to a…

Analysis of PDEs · Mathematics 2020-10-22 Tania Biswas , Elisabetta Rocca

In this article we propose an inverse analysis algorithm to find the best fit of multiple material parameters in different coupled multi-physics biofilm models. We use a nonlinear continuum mechanical approach to model biofilm deformation…

Computational Engineering, Finance, and Science · Computer Science 2022-12-26 Harald Willmann , Wolfgang A. Wall

The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…

Optimization and Control · Mathematics 2022-05-03 Cornel Marius Murea , Dan Tiba

The aim of this paper is to adapt the general multitime maximum principle to a Riemannian setting. More precisely, we intend to study geometric optimal control problems constrained by the metric compatibility evolution PDE system; the…

Optimization and Control · Mathematics 2012-10-22 Andreea Bejenaru , Constantin Udriste