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- Title
The behavior of solutions of nonlinear reaction-diffusion PDE's relation to dynamics of propagation of cancer.
- Authors
Soltanov, Kamal N.
- Abstract
In this paper, we propose a new mathematical model of nonlinear reaction-diffusion PDE's describing the dynamics of the propagation of cancer. By applying obtained results conclusions on the dynamics of the propagation of cancer are drawn. These problems have nonlocal nonlinearity with variable exponents and possess special properties: these can be to remain either dissipative all time or become non-dissipative after a finite time. Here the solvability and behavior of solutions are proved when problems are yet dissipative and when become nondissipative. It is shown that if the studied process gets become nondissipative can have various states, e.g. an infinite number of different unstable solutions with varying speeds, in addition, their propagation can become chaotic. Investigation of this mathematical model allows explaining the dynamics of the propagation of cancer.
- Subjects
MATHEMATICAL models; REACTION-diffusion equations
- Publication
Nonlinear Studies, 2023, Vol 30, Issue 3, p883
- ISSN
1359-8678
- Publication type
Article