Agnieszka Bartłomiejczyk, Marek Bodnar, Magdalena U. Bogdańska, M. Piotrowska
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引用次数: 0
Abstract
Abstract Low-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the basic mathematical properties of the model, we study the possibility of the existence of travelling wave solutions in the framework of Fenichel’s invariant manifold theory. The estimates of the minimum speeds of the travelling wave solutions are provided. The obtained analytical results are illustrated by numerical simulations.
期刊介绍：
The International Journal of Applied Mathematics and Computer Science is a quarterly published in Poland since 1991 by the University of Zielona Góra in partnership with De Gruyter Poland (Sciendo) and Lubuskie Scientific Society, under the auspices of the Committee on Automatic Control and Robotics of the Polish Academy of Sciences.
The journal strives to meet the demand for the presentation of interdisciplinary research in various fields related to control theory, applied mathematics, scientific computing and computer science. In particular, it publishes high quality original research results in the following areas:
-modern control theory and practice-
artificial intelligence methods and their applications-
applied mathematics and mathematical optimisation techniques-
mathematical methods in engineering, computer science, and biology.
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