Related papers: Long-time Dynamics and Optimal Control of a Diffus…
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 study the optimal control problem of a free boundary PDE model describing the growth of multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor…
We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…
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…
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
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…
We consider a system of two coupled integro-differential equations modelling populations of healthy and cancer cells under therapy. Both populations are structured by a phenotypic variable, representing their level of resistance to the…
This paper is intended to tackle the control problem associated with an extended phase field system of Cahn-Hilliard type that is related to a tumor growth model. This system has been investigated in previous contributions from the…
We propose a diffuse interface model to describe tumor as a multicomponent deformable porous medium. We include mechanical effects in the model by coupling the mass balance equations for the tumor species and the nutrient dynamics to a…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
In the present contribution we study the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a viscous Cahn-Hilliard type equation for the phase variable with a reaction-diffusion equation for the…
Mathematical models that describe the tumor growth process have been formulated by several authors in order to understand how cancer develops and to develop new treatment approaches. In this study, it is aimed to investigate the long-time…
In this paper, we study an optimal control problem for a macroscopic mechanical tumour model based on the phase field approach. The model couples a Cahn--Hilliard type equation to a system of linear elasticity and a reaction-diffusion…
A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-cancer therapies such as surgery and chemical treatments…
In this paper, we study an optimal control problem for a brain tumor growth model that incorporates lactate metabolism, viscoelastic effects, and tissue damage. The PDE system, introduced in [G. Cavalleri, P. Colli, A. Miranville, E. Rocca,…
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…
The interactions between tumor cells and the immune system play a crucial role in cancer evolution. In this study, we explore how these interactions influence cancer progression by modeling the relationships among naive T cells, effector T…
We propose a new type of diffuse interface model describing the evolution of a tumor mass under the effects of a chemical substance (e.g., a nutrient or a drug). The process is described by utilizing the variables $\varphi$, an order…
In this paper, we address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of chemotaxis into account. The system describing the evolution…
In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…