相关论文: Local asymptotics and optimal control for a viscou…

In this paper, we address an optimal distributed control problem for a non-local model of phase-field type, describing the evolution of tumour cells in presence of a nutrient. The model couples a non-local and viscous Cahn-Hilliard equation…

We consider a non-local tumour growth model of phase-field type, describing the evolution of tumour cells through proliferation in presence of a nutrient. The model consists of a coupled system, incorporating a non-local Cahn-Hilliard…

We consider a particular phase field system which physical context is that of tumor growth dynamics. The model we deal with consists of a Cahn-Hilliard type equation governing the evolution of the phase variable which takes into account 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…

We consider a local Cahn-Hilliard-type model for tumor growth as well as a nonlocal model where, compared to the local system, the Laplacian in the equation for the chemical potential is replaced by a nonlocal operator. The latter is…

This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…

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…

A distributed optimal control problem for a phase field system which physical context is that of tumor growth is discussed. The system we are going to take into account consists of a Cahn-Hilliard equation for the phase variable (relative…

We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong…

This paper investigates an optimal control problem associated with a two-dimensional multi-species Cahn-Hilliard-Keller-Segel tumor growth model, which incorporates complex biological processes such as species diffusion, chemotaxis,…

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…

We study a Cahn-Hilliard-Darcy system with mass sources, which can be considered as a basic, though simplified, diffuse interface model for the evolution of tumor growth. This system is equipped with an impermeability condition for 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…

We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…

In the present work, we develop a comprehensive and rigorous analytical framework for a non-local phase-field model that describes tumour growth dynamics. The model is derived by coupling a non-local Cahn-Hilliard equation with a parabolic…

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…

We consider a diffuse interface model for tumor growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation, which models a tumor growing in the presence of a nutrient species and surrounded by…

We study a distributed optimal control problem for a nonisothermal Caginalp-type phase-field model that describes tumour growth under thermal therapy. The PDE system couples a possibly viscous Cahn-Hilliard equation, governing the evolution…

In this work, we investigate a distributed optimal control problem for an extended phase field system of Cahn--Hilliard type which physical context is that of tumor growth dynamics. In a previous contribution, the author has already studied…

In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumour cells coupled to a reaction-diffusion type equation for the nutrient density and a Brinkman-type equation for the velocity. We equip…