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We consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution of different subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth equation is introduced to model the evolution of the moving… (More)

In this paper we study a system of equations concerning equilibrium positions of journal bearings. The problem consists of two surfaces in relative motion separated by a small distance filled with a lubricant. The shape of the inlet surface is circular, while the other surface has a more general shape. Our result shows the existence of at least one… (More)

It is well-known that the pressure of a lubricating fluid filling the gap between two solid surfaces satisfies the Reynolds equation involving the distance function, h, between both planes, as a crucial coefficient. Nevertheless, in most of the applications the function h is not known a priori. Here we consider the simple case in which the surfaces are two… (More)

The immunotherapy using dendritic cells (DCs) against different varieties of cancer is an approach that has been previously explored which induces a specific immune response. This work presents a mathematical model of DCs immunotherapy for melanoma in mice based on work by Experimental Immunotherapy Laboratory of the Medicine Faculty in the Universidad… (More)

We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model… (More)

- J I D Az, J I Tello
- 2007

We study a model of growth of tumors with two free boundaries: an inner boundary delaying the necrotic zone and the outer boundary delaying the tumor. We take into account the presence of inhibitors and its interaction with the nutrients. We show the existence and uniqueness of the solution of the model under suitable conditions on the inhibitors… (More)

- J Ignacio Tello
- 2007

We consider a limit case of a system of two equations arising in magnetic recording for a one-dimensional domain. The system models the tape deflection when it is driven over a magnetic head profile, which is a known function. The system is reduced to a second order nonlinear equation, where the unknown u appears evaluated in a finite set of distinguished… (More)