Currently displaying 1 – 3 of 3

Showing per page

Order by Relevance | Title | Year of publication

Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model

Maciej CytowskiAkio ItoMarek Niezgódka — 2009

Banach Center Publications

In the present paper, we consider an approximate system of one-dimensional simplified tumor invasion model, which was originally proposed by Chaplain and Anderson in [chaplain-anderson-03]. The simplified tumor invasion model is composed of PDE and ODE. Actually, the PDE is the balance equation of the density of tumor cells and the ODE describes the dynamics of concentration of extracellular matrix. In this model, we take into account that the random motility of the density of tumor cells is given...

A phase-field model of grain boundary motion

Akio ItoNobuyuki KenmochiNoriaki Yamazaki — 2008

Applications of Mathematics

We consider a phase-field model of grain structure evolution, which appears in materials sciences. In this paper we study the grain boundary motion model of Kobayashi-Warren-Carter type, which contains a singular diffusivity. The main objective of this paper is to show the existence of solutions in a generalized sense. Moreover, we show the uniqueness of solutions for the model in one-dimensional space.

Page 1

Download Results (CSV)