Multi-layered tumor cell cultures with almost periodic nutrient supply

Modeling of multi-layered cell cultures (MCC) assume flat geometry in a 3D tumor growth model.Some results available in the time-dependent framework assume a periodic nutrient supply $\Phi(t)$. Our aim is to generalize such considerations. Namely, we show that a stable oscillating tumor growth arises in the long term, whenever the mean value of the almost periodic nutrient supply $\overline{\Phi}$ surpasses certain threshold level, $\overline{\Phi}>\tilde{\sigma}$. Meanwhile, a vanishing tumor is predicted in the complementary case, $\overline{\Phi}\leq \tilde{\sigma}$.