EXISTENCE OF TRAVELING WAVE SOLUTIONS TO DATA-DRIVEN GLIOBLASTOMA MULTIFORME GROWTH MODELS WITH DENSITY-DEPENDENT DIFFUSION
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Date
2020-10-23
Authors
Kashkynbayev, Ardak
Amanbek, Yerlan
Shupeyeva, Bibinur
Kuang, Yang
Journal Title
Journal ISSN
Volume Title
Publisher
AIMS Press
Abstract
Mathematical modeling for cancerous disease has attracted increasing attention from the
researchers around the world. Being an effective tool, it helps to describe the processes that happen
to the tumour as the diverse treatment scenarios. In this paper, a density-dependent reaction-diffusion
equation is applied to the most aggressive type of brain cancer, Glioblastoma multiforme. The model
contains the terms responsible for the growth, migration and proliferation of the malignant tumour.
The traveling wave solution used is justified by stability analysis. Numerical simulation of the model
is provided and the results are compared with the experimental data obtained from the reference papers.
Description
Keywords
reaction-diffusion equation, traveling wave solution, glioblastoma, tumor growth, stability, Research Subject Categories::MATHEMATICS
Citation
Kashkynbayev, A., Amanbek, Y., Shupeyeva, B., & Kuang, Y. (2020). Existence of traveling wave solutions to data-driven glioblastoma multiforme growth models with density-dependent diffusion. Mathematical Biosciences and Engineering, 17(6), 7234–7247. https://doi.org/10.3934/mbe.2020371