Existence and uniqueness of solutions for a random PDE-ODE model describing glioma invasion and radiotherapy

We study a stochastic model for the growth and invasion of glioma cells in the anisotropic brain tissue, also incorporating effects of radiotherapeutic interventions and associated uncertainties. The PDE-ODE model couples glioma and healthy tissue dynamics in a nonlinear manner and explicitly includes treatment-related stochasticity through random depletion terms. The macroscopic system has been obtained by an upscaling procedure from a microscopic description in [1]. We prove the existence and uniqueness of local strong solutions to the corresponding stochastic system. The analysis addresses challenges arising from the nonlinear coupling, anisotropic diffusion, taxis mechanisms, and stochastic treatment effects, providing a first rigorous step toward the mathematical understanding of stochastic continuum models for glioma invasion and therapy response.