(ScienceDirect, 2020-05-27) Benito Muñoz, Juan J.; García Hernández, Miguel Ángel; Gavete Corvinos, Luis Antonio; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio Manuel; https://orcid.org/0000-0002-9092-9619; https://orcid.org/0000-0001-6581-5671; https://orcid.org/0000-0003-0533-3464
We study a mathematical model of cancer cell invasion of tissue (extracellular matrix) consisting of a system of reaction-diffusion-taxis partial differential equations which describes the interactions between cancer cells, the matrix degrading enzyme and the host tissue. We analyze the local stability of the constant equilibrium solutions to the chemotaxis-haptotaxis system, we derive a discretization of the system by means of the Generalized Finite Difference Method (GFDM) and we prove the convergence of the discrete solution to the analytical one. Also, we provide several numerical examples on the applications of this meshless method over regular and irregular domains.
