Lower bounds for the finite-time blow-up of solutions of a cancer invasion model

In this article, we consider non-negative solutions of the nonlinear cancer invasion mathematical model involving proliferation and growth functions with homogeneous Neumann and Robin type boundary conditions. We first obtain lower bounds for the finite time blow-up of solutions in $\mathbb{R}^3$ wi...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2019-01, Vol.2019 (12), p.1-13
Main Authors: Shangerganesh, Lingeshwaran, Sathishkumar, Govindharaju, Karthikeyan, Shanmugasundaram
Format: Article
Language:English
Subjects:
blow up
cancer invasion
lower bounds
reaction-diffusion
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Summary:In this article, we consider non-negative solutions of the nonlinear cancer invasion mathematical model involving proliferation and growth functions with homogeneous Neumann and Robin type boundary conditions. We first obtain lower bounds for the finite time blow-up of solutions in $\mathbb{R}^3$ with assumed boundary conditions. Finally, we extend the blow-up results of the given system in $\mathbb{R}^2$ using first-order differential inequality techniques and under appropriate assumptions on data.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2019.1.12