467 research outputs found
Analysis of a mathematical model for the growth of cancer cells
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 cell dead. The growth process is caused by a diffusing nutrient
concentration and is controlled by an internal cell pressure . We
assume that the tumor occupies a strip-like domain with a fixed boundary at
and a free boundary , where is a -periodic
function. First, we prove the existence of solutions and that
the model allows for peculiar stationary solutions. As a main result we
establish that these equilibrium points are locally asymptotically stable under
small perturbations.Comment: 15 pages, 2 figure
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