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

• Main Authors: Lingeshwaran Shangerganesh, Govindharaju Sathishkumar, Shanmugasundaram Karthikeyan
• Format: Article
• Language: English
• Published: University of Szeged 2019-02-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: blow up; lower bounds; cancer invasion; reaction-diffusion
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=7317

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.