Model order reduction of tumor growth model

In this paper, reduced order models (ROMs) for the tumor growth model, which is a nonlinear cross-diffusion system are presented. Linear-quadratic ordinary differential equations are obtained by applying the finite difference method to the tumor growth model for spatial discretization. The structure of the ROMs is the same as the structure of the full order model. Proper orthogonal decomposition method with tensorial form is sufficient to compute the reduced solutions efficiently and fast. The results of ROM are presented for one-and two-dimensional cases. Finally, the entropy structure for the reduced solutions, which are in decay form are presented