Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers.

The known three-component reaction-diffusion system modeling competition and co-existence of different language speakers is under study. A modification of this system is proposed, which is examined by the Lie symmetry method; furthermore, exact solutions in the form of traveling fronts are constructed and their properties are identified. Plots of the traveling fronts are presented and the relevant interpretation describing the language shift that has occurred in Ukraine during the Soviet times is suggested.

Distributed modeling of glucose-induced osmotic flow.

We investigated a distributed model for the transport of fluid and glucose that allows for the description of hydrostatic pressure, interstitial fluid void volume, and glucose profiles in the tissue. Computer simulations for conditions mimicking the initial minutes of a peritoneal dialysis dwell with 3.86% glucose demonstrated that the rate of fluid flow to the peritoneal cavity was sensitive mostly to the reflection coefficient for glucose in the capillary wall, sigmaCG, whereas the hydrostatic pressure in deep tissue layers was sensitive to the reflection coefficient for glucose in the interstitium, sigmaTG. For hydrostatic pressure in the peritoneal cavity equal to 12 mmHg, sigmaCG = 0.5, sigmaTG = 0.005, and other parameters taken from published physiologic data, the rate of ultrafiltration was about 9 mL/min. Glucose concentration and hydrostatic pressure in the tissue increased in a layer less than 2 mm from the peritoneal cavity; deeper layers were close to their equilibrium values. If a high-value osmotic coefficient for the capillary wall is assumed, the proposed model describes hydrostatic pressure and glucose profiles that agree with available data.