Abstract
In this paper, we study the linear stability of the free boundary problem for tumors. The model is a coupled system of PDE with Robin boundary, which involves concentration of nutrients, concentration of inhibitor and pressure. The presence of inhibitor in this model affects the diffusion of nutrient. We establish the existence and uniqueness of the radially-symmetric solution (us,vs,ps,Rs). We further prove that there exists a threshold value μ⁎ such that (us,vs,ps,Rs) is linearly stable under non-radially symmetric perturbations for μ∈(0,μ⁎) and linearly unstable for μ>μ⁎.
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