Publication at Faculty of Mathematics and Physics |
2013
Abstract
The paper analyzes basic mathematical questions for a model of chemically reacting mixtures. We derive a model of several (finite) component compressible gas taking rigorously into account the thermodynamical regime.
Mathematical description of the model leads to a degenerate parabolic equation with hyperbolic deviation. The thermodynamics implies that the diffusion terms are non-symmetric, not positively defined, and cross-diffusion effects must be strongly marked.
The mathematical goal is to establish the existence of weak solutions globally in time for arbitrary number of reacting species. A key point is an entropy-like estimate showing possible renormalization of the system.