Abstract
Lower bounds for the finite-time blow-up of solutions of a cancer invasion model
Highlights
Cancer is the most threatening disease to the society due its mortality rate among affected patients
In the past few years, many works presented for the acid-mediated invasion hypothesis and it is proposing that tumour acidification confers an advantage to the tumor cells by producing a harsh environment
Partial differential equation (PDE) have been used for many cancer invasion mathematical models, for example, see [2, 4, 5, 7, 10, 15, 24–28] and the references therein
Summary
Cancer is the most threatening disease to the society due its mortality rate among affected patients. This paper investigate the properties of non-negative solutions of the following nonlinear coupled cancer invasion mathematical model in a smooth bounded domain Ω ⊂ RN, N = 2, 3 : ut − d1∆u = μu(1 − u − v) vt = −kvw + ρv(1 − u − v) wt − d2∆w = ζu(1 − w) − νw in Ω × (0, I), in Ω × (0, I),. The decay and growth rates of MDEs are respectively modeled by νw and ζu(1 − w), where ν, ζ are positive constants. In line with these motivations, in this work, we estimate the lower bounds for the finite time blow-up of solutions in RN, N = 2, 3 with Neumann and Robin type boundary conditions for cancer invasion reaction-diffusion system (1.1) using first-order differential inequality techniques.
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