Studies in generalized hydrodynamics for chemical reactions and shock waves

This thesis is made of two parts. In the first part, we study pattern formations and dissipation of energy and matter by using hyperbolic reaction-diffusion equations for reacting systems. Two-dimensional hyperbolic reaction-diffusion equations are numerically solved for the Selkov model and the Brusselator. It is shown that the evolution equations used can give rise to various kinds of patterns such as hexagonal structures, stripes, maze structures, chaotic structures, etc., depending on the values of the reaction-diffusion number and the initial and boundary conditions. The values of the entropy production computed indicate that the system maintains the particular organized local structures at the expense of energy and matter. However, when the system produces a chaotic pattern, the entropy production is lower than the locally organized structures. The phase speed of travelling oscillating chemical waves can be obtained from the linearized hyperbolic reaction-diffusion equations. The Luther-type speed formula is obtained in the lowest order approximation in the case of the Brusselator. The two-dimensional power spectra computed for chaotic patterns still preserve some kind of symmetry.In the second part of this thesis, the generalized hydrodynamics is applied to calculate the shock profiles, shock widths, and calortropy production for a Maxwell gas. Shock solutions are shown to exist for all Mach numbers. This is in contrast to the Grad moment equation method which does not admit shock solution for $N sb{M} ge 1.65$ and to the method of Anile and Majorana which breaks down for $N sb{M} ge 2.09.$ The energy dissipation in the shock is shown to increase with the Mach number as a power law of the form $(N sb{M} - a) sp{ alpha}$ where a and $ alpha$ are real constants