The glioblastoma Multiforme (GBM) is a type of cerebral tumor that belongs to the gliomas' group. It is notorious for its high malignancy in humans, typically resulting in a life expectancy of only 14.6 months with standard treatments. Furthermore, GBM is among the most common brain tumors, accounting for 45.66% occurrence of all cerebral tumors, and it has an exceptionally high recurrence rate from 90% to 100%

Gliomas represent a group of malignant tumors that can originate in any part of the central nervious system (CNS), which includes the brain and, less frequently, the medullary spine. These tumors are characterized by their infiltrative growth and tendency to spread within the CNS. These tumors are classified as unifocal when a single tumoral mass is present in the patient, and multifocal when there are two or more independent tumoral masses.

Due to the complex dynamics of the glioblastomas, any attempt to model this behaviour is of utmost importance. The objective of this project is to understand the description of the following model and develop it to gain insights into its behaviour.

• Study the biophysical process associated with the growth of brain tumors, and its modeling through a system of partial differential equations.

• Computationally implement a numerical simulation that allows approximating the solutions of the model

• Analyze the asymptotic behavior of the classical solution of the system