Team dracula

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Section: New Results

Nonlinear dynamics of travelling waves for reaction-diffusion equations

Existence of waves for a nonlocal reaction-diffusion equation

Participant : Vitaly Volpert.

In collaboration with I. Demin (Novartis Pharma in Basel, Switzerland).

We studied in [17] a nonlocal reaction-diffusion equation arising in population dynamics. The integral term in the nonlinearity describes nonlocal stimulation of reproduction. We proved existence of travelling wave solutions by the Leray-Schauder method using topological degree for Fredholm and proper operators and special a priori estimates of solutions in weighted Hölder spaces.

Keywords: integro-differential equation, travelling waves, Leray-Schauder method.

Linear stability analysis of reaction fronts propagation in liquids with vibrations

Participant : Vitaly Volpert.

In collaboration with K. Allali, F. Bikany and A. Taik (University of Mohammedia, Morocco).

Influence of vibrations on the onset of convective instability of reaction fronts in a liquid medium was studied in [14] . The model consisted of a reaction-diffusion system coupled with the Navier-Stokes equations under the Boussinesq approximation. Linear stability analysis of the problem was fulfilled, and the convective instability boundary was found.

Keywords: convective instability, reaction front propagation, vibrations.


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