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Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…

In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular…

In this paper, we study a nonlocal boundary blow up problem on an interval and obtain the precise asymptotic formula for solutions when the bifurcation parameter in the problem is large.

The uncontrolled proliferation of cancer cells and their interaction with healthy tissue poses a major challenge in oncology. This manuscript develops and analyzes mathematical models that describe tumor response to radiotherapy by…

Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones contain competition for space using purely fluid mechanical…

The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical…

We address numerical challenges in solving hyperbolic free boundary problems described by spherically symmetric conservation laws that arise in the modeling of tumor growth due to immune cell infiltrations. In this work, we normalize the…

We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the…

The aim of this paper is to investigate the asymptotic behavior of a biphase tumor fluid flow derived by 2-scale homogenisation techniques in recent works. This biphase fluid flow model accounts for the capillary wall permeability, and the…

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 consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff (incompressible) limit in a porous medium type problem with a Lotka-Volterra…

We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least…

We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations, the following alternative holds: either the shape…

The existence of stationary radial solutions to a partial differential equation arising in the theory of epitaxial growth is studied. Our results depend on the size of a parameter that plays the role of the velocity at which mass is…

We study a free transmission problem in which solution minimizes a functional with different definitions in positive and negative phase of function. We prove some asymptotic regularity results when the jumps of the diffusion coefficients…

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical properties of living tissues. These two classes of models can be related using a stiff pressure law. In the incompressible…

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…

The well known nonlinear model for describing the solid tumour growth [Byrne HM., et al. Appl Math Letters 2003;16:567-74] is under study using an approach based on Lie symmetries. It is shown that the model in the two-dimensional (in…

In this paper, we study a tumor growth model where the growth is driven by nutrient availability and the tumor expands according to Darcy's law with a mechanical pressure resulting from the incompressibility of the cells. Our focus is on…