A difference scheme for solving the equations of tumor growth subject to the restricted flow of motile cells

The article investigates one-dimensional mathematical model of tumor growth represented by a system of quasi-linear parabolic equations. We assume certain restrictions 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.