Premium
On the multiplicity of solutions of a simplified tumor growth model with a free boundary
Author(s) -
Bensid Sabri,
Chekroun Abdennasser
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5940
Subject(s) - multiplicity (mathematics) , mathematics , mathematical analysis , boundary value problem , nonlinear system , boundary (topology) , free boundary problem , domain (mathematical analysis) , physics , quantum mechanics
We consider a mathematical model of tumor growth taking into account the spatial structure and include a different phases because of the lack of the nutriments. This model is expressed as a PDE on a spherical domain describing the tumor region. The nonlinearity of this PDE is discontinuous, and our problem can be regarded as a free boundary problem. In fact, the boundary of the tumor and another part in the interior are unknown. We obtain a multiplicity result of solutions together with some properties of the associated free boundaries.