Biomedical subjects
Publications and source records attributed to Vitaly Volpert.
A model illustrating Darwin's divergence principle is presented. It shows how competition for resources can explain evolutionary branching. It is based on an assumption of degenerate competition. Mathematically, it is a partial differential equation with an integral term, and it describes a new mechanism of self-organization.
The work is devoted to numerical simulations of the interaction of heat explosion with natural convection. The model consists of the heat equation with a nonlinear source term describing heat production due to an exothermic chemical reaction coupled with the Navier-Stokes equations under the Boussinesq approximation. We show how complex regimes appear through successive bifurcations leading from a stable stationary temperature distribution without convection to a stationary symmetric convective solution, stationary asymmetric convection, periodic in time oscillations, and finally aperiodic oscillations. A simplified model problem is suggested. It describes the main features of solutions of the complete problem.