Glioblastoma (GBM) is a highly aggressive brain tumor whose proliferation is classically modeled using reaction-diffusion partial differential equations (PDEs). While traditional mesh-based numerical solvers provide accurate approximations, they yield purely discrete solutions. This paper proposes a mesh-free computational framework to simulate the 2D spatio-temporal invasion of GBM using Physics-Informed Neural Networks (PINNs) and Extended PINNs (XPINNs). To address network convergence failures caused by sharp gradients and discontinuous initial conditions, we introduce a logistic smoothing strategy coupled with domain non-dimensionalization. Furthermore, an XPINN architecture is implemented to decompose the computational domain, enabling parallelization and significantly accelerating the training process. Unlike classical numerical methods, the proposed deep learning approach yields a continuous, closed-form surrogate solution, allowing for instant tumor density predictions at any arbitrary time and location without the need for post-hoc interpolation. This framework demonstrates the viability and computational efficiency of domain-decomposed physics-informed learning for analyze the tumor dynamics.