Biomedical subjects

S Fedotov

Publications and source records attributed to S Fedotov.

3 recordsLinked to original sources

PubMed2001

Front propagation into an unstable state of reaction-transport systems.

We studied the propagation of traveling fronts into an unstable state of the reaction-transport systems involving integral transport. By using a hyperbolic scaling procedure and singular perturbation techniques, we determined a Hamiltonian structure of reaction-transport equations. This structure allowed us to derive asymptotic formulas for the propagation rate of a reaction front. We showed that the macroscopic dynamics of the front are "nonuniversal" and depend on the choice of the underlying random walk model for the microscopic transport process.

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PubMed1999

Wave front for a reaction-diffusion system and relativistic Hamilton-Jacobi dynamics.

The problem of wave-front propagation for the n-dimensional reaction-diffusion system involving Kolmogorov-Petrovskii-Piskunov kinetics and the diffusion transport with a finite velocity has been considered. By using a scaling procedure we have given an asymptotic derivation of the equation governing the evolution of a reaction front in the long-time large-distance limit. It has been found that this equation is identical in form to the relativistic Hamilton-Jacobi equation. In the case of a constant value of chemical rate function we have derived exact formulas for the position of reaction front and the speed of propagation by using relativistic mechanics techniques.

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PubMed1999

Nonuniform reaction rate distribution for the generalized Fisher equation: ignition ahead of the reaction front.

We have addressed the problem of wavefront propagation for the generalized Fisher equation involving diffusion transport with a finite velocity and a spatially nonuniform reaction rate. We have considered in detail the phenomenon of wavefront jump or ignition ahead of the reaction front for a piecewise constant reaction rate. By using a relativistic mechanics technique based on the principle of least action we have found the criterion under which the ignition phenomenon happens and the time of appearance of the new front ahead of the initial reaction front.

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