Analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis. (English) Zbl 1392.35322
This work addresses a mathematical background of one of the models of tumor growth given as a system of free boundary problem for partial differential equations. The key feature of such kind of models is the proper choice of boundary conditions, which should be realistic from the biological point of view and, simultaneously, assure correct (i.e. robust, unique, etc.) mathematical solutions. The authors consider the so-called Robin boundary conditions, which balance the outflow of nutrients located inside of the tumor with the concentration of nutrients in the host tissue.
Within this problem statement, existence, uniqueness, and local well-posedness were studied as well as the asymptotic stability of the radial stationary solution under radial and non-radial perturbations.
Within this problem statement, existence, uniqueness, and local well-posedness were studied as well as the asymptotic stability of the radial stationary solution under radial and non-radial perturbations.
Reviewer: Eugene Postnikov (Kursk)
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92C37 | Cell biology |
| 35R35 | Free boundary problems for PDEs |
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
free boundary problem; tumor growth; well-posedness; stationary solution; asymptotic stabilityReferences:
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