Geodesic
A difference scheme for solving the equations of tumor growth subject to the restricted flow of motile cells
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 2, pp. 98-106

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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.
Keywords: difference scheme; substrate taxis; the problem with movable boundary; break allocation. 
@article{VYURU_2017_10_2_a7,
     author = {L. S. Isachenko and A. I. Lobanov},
     title = {A difference scheme for solving the equations of tumor growth subject to the restricted flow of motile cells},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {98--106},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_2_a7/}
}
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L. S. Isachenko; A. I. Lobanov. A difference scheme for solving the equations of tumor growth subject to the restricted flow of motile cells. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 2, pp. 98-106. http://geodesic.mathdoc.fr/item/VYURU_2017_10_2_a7/