Volume 10, no. 2Pages 98 - 106
A Difference Scheme for Solving the Equations of Tumor Growth Subject to the Restricted Flow of Motile CellsL.S. Isachenko, L.I. Lobanov
The article investigates one-dimensional mathematical model of tumor growth represented by a system of quasi-linear parabolic equations. We assume certain restrictions Full text
on the full flow of the motile tumor cells, leading to the possible degeneration of the system into a hyperbolic type and emergence of discontinuous (weak) solution. To find weak solution we consider tumor growth as the emergence of a new phase. Thus we have a generalized (nonlinear) Stefan problem. The authors propose and implement a difference scheme with the explicit statement of the phase-change moving boundary to solve the problem. It is shown that this approach allows to describe different regimes of tumor growth.
- difference scheme; substrate taxis; the problem with movable boundary; break allocation.
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