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Travelling waves for low-grade glioma growth and response to a chemotherapy model

Bartłomiejczyk Agnieszka, Bodnar Marek, Bogdańska Magdalena U., Piotrowska Monika J.

International Journal of Applied Mathematics and Computer Science

2023

Vol. 33, no. 4

569--581

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.

Note of the full generalized models of the extensions of a logic

Albuquerque H., Font J. M., Jansana R.

Reports on Mathematical Logic

2017

Vol. 52

57--68

In this short note we show that the full generalized models of any extension of a logic can be determined from the full generalized models of the base logic in a simple way. The result is a consequence of two central theorems of the theory of full generalized models of sentential logics. As applications we investigate when the full generalized models of an extension can also be full generalized models of the base logic, and we prove that each Suszko lter of a logic determines a Suszko lter of each of its extensions, also in a simple way.