Stability for Periodic Solution for a Free‐Boundary Vascular Tumor Model

ABSTRACT A small coefficient describing the relationship between nutrient diffusion and tumor growth is set to zero in many papers in the literature. If is not zero, the global asymptotic stability for radially symmetric periodic solutions was established in [13] for a tumor immersed in a periodic nutrient supply (Dirichlet periodic boundary condition) and for a vascular tumor (Robin boundary condition) in [15]. In this paper, we study the periodic radially symmetric solution for the vascular tumor model. When perturbed with non‐radially symmetric data, we establish a criterion to determine the linear stability for the parameter . Furthermore, the instability arises from the 2‐mode.