Analysis of a Radiotherapy Model for Brain Tumors
ABSTRACT In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors undergoing radiotherapy treatment. Under certain assumptions regarding the given data in the model, we prove the existence and uniqueness of a weak nonnegative (biologically relevant) solution. Then, we show how the additional regularity of initial data affects the regularity of these solutions. Besides, we analyze the optimal control of the advection coefficient which tunes the radiotherapy effect on the tumor cell population. We also complement our analytical results with relevant numerical simulations.
Authors
- Roman M. Taranets (ORCID: https://orcid.org/0000-0002-9177-5500)
- Hangjie Ji (ORCID: https://orcid.org/0000-0001-7613-8522)
- Nataliya Vasylyeva (ORCID: https://orcid.org/0000-0002-8623-5921)
- Marina Chugunova (ORCID: https://orcid.org/0000-0002-2045-6684)
Institutions
- Claremont Graduate University (US)
- North Carolina State University (US)
- Institute of Applied Mathematics and Mechanics (UA)
- S.P. Timoshenko Institute of Mechanics (UA)
- Politecnico di Milano (IT)
Publication Details
- Journal
- Studies in Applied Mathematics
- Published
- 2025-07-01
- DOI
- https://doi.org/10.1111/sapm.70074
- Primary Topic
- Mathematical Biology Tumor Growth
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Research Foundation of Ukraine