{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:46:03Z","timestamp":1760143563381,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,3]],"date-time":"2024-02-03T00:00:00Z","timestamp":1706918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education and Science of Ukraine","award":["0123U101691"],"award-info":[{"award-number":["0123U101691"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>A simple cell population growth model is proposed, where cells are assumed to have a physiological structure (e.g., a model describing cancer cell maturation, where cells are structured by maturation stage, size, or mass). The main question is whether we can guarantee, using the death rate as a control mechanism, that the total number of cells or the total cell biomass has prescribed dynamics, which may be applied to modeling the effect of chemotherapeutic agents on malignant cells. Such types of models are usually described by partial differential equations (PDE). The population dynamics are modeled by an inverse problem for PDE in our paper. The main idea is to reduce this model to a simplified integral equation that can be more easily studied by various analytical and numerical methods. Our results were obtained using the characteristics method.<\/jats:p>","DOI":"10.3390\/computation12020026","type":"journal-article","created":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T08:41:43Z","timestamp":1707122503000},"page":"26","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Mathematical Modeling of Cell Growth via Inverse Problem and Computational Approach"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6601-4374","authenticated-orcid":false,"given":"Ivanna","family":"Andrusyak","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9886-3589","authenticated-orcid":false,"given":"Oksana","family":"Brodyak","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0359-5025","authenticated-orcid":false,"given":"Petro","family":"Pukach","sequence":"additional","affiliation":[{"name":"Department of Computational Mathematics and Programming, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7818-7755","authenticated-orcid":false,"given":"Myroslava","family":"Vovk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Brauer, F., and Castillo-Chavez, C. 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