Existence and uniqueness of solutions for a random PDE-ODE model describing glioma invasion and radiotherapy
Abstract
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.
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BibTeX
@misc{conte2026existence,
title = {{Existence and uniqueness of solutions for a random PDE-ODE model describing glioma invasion and radiotherapy}},
author = {Martina Conte and Sandesh Athni Hiremath and Christina Surulescu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35763},
eprint = {2610.35763},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35763},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Existence and uniqueness of solutions for a random PDE-ODE model describing glioma invasion and radiotherapy
AU - Martina Conte
AU - Sandesh Athni Hiremath
AU - Christina Surulescu
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35763
UR - https://arxiv.org/abs/2610.35763
AB - 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.
ER -