Related papers: Un mod\`ele non-lin\'eaire de prolif\'eration cell…
We analyse the asymptotic behaviour of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial…
In this paper, we investigate a system of two nonlinear partial differential equations, arising from a model of cellular proliferation which describes the production of blood cells in the bone marrow. Due to cellular replication, the two…
In this paper, we investigate a nonlinear partial differential equation, arising from a model of cellular proliferation. This model describes the production of blood cells in the bone marrow. It is represented by a partial differential…
This paper is devoted to the analysis of a mathematical model of blood cells production in the bone marrow (hematopoiesis). The model is a system of two age-structured partial differential equations. Integrating these equations over the…
This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
In this paper we propose an existence and uniqueness theory for the solutions of a system of non-linear hyperbolic conservation laws, structured in age and maturity variables, representing a tissue environment. In particular we are…
We demonstrate aging behavior in a simple non-linear system. Our model is a chaotic map which generates deterministically sub-diffusion. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks,…
Disordered solids often change their elastic response as they slowly age. Using experiments and simulations, we study how aging disordered planar networks under an applied stress affects their nonlinear elastic response. We are able to…
The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other…
We analyze a multi-type age dependent model for cell populations subject to unidirectional motion, in both a stochastic and deterministic framework. Cells are distributed into successive layers; they may divide and move irreversibly from…
We investigate a model of cell division in which the length of telomeres within the cell regulate their proliferative potential. At each cell division the ends of linear chromosomes change and a cell becomes senescent when one or more of…
We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times…
This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the…
This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…
All types of blood cells are formed by differentiation from a small self-maintaining population of pluri-potential stem cells in the bone marrow. Despite abundant information on the molecular aspects of division, differentiation, commitment…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in…
Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…