Global Solutions And Their Structural Evolution Of Multi-dimensional Chapman-Jouguet Equations

In this paper, we investigate the multi-dimensional Chapman-Jouguet combustion models, construct the global solutions and analyze their structural evolution. There are two important phe-nomena in combustion reaction, detonation and deflagration. They are reasonably explained by Chapman-Jouguet theory and Zeldovich-von Neumann-Doring theory. There are many significant work on these theories. However, these works focus on one-dimensional combustion models. Re-searches on multi-dimensional models, especially on the structure of their solutions are few. The equations are very hard to be solved due to lack of new approaches and the complex structure of multi-dimensional solutions.We study a class of Riemann problems of two-dimensional Chapman-Jouguet equations in Chapter4. The initial data have two pieces of constant states, which are separated by a convex discontinuity. We construct a class of two-dimensional non-selfsimilar solutions of combustion equations, and therefore discover their structure and evolution, as well as the essential difference between our2-D solutions and one-dimensional solutions.In Chapter5we construct self-similar solutions of3-D Chapman-Jouguet equations. We reduce the dimensions of equation by self-similar transformation. But there are still three variables remain. So it is still an essential and difficult multi-dimensional problem. Specially we consider the cases that reactant is ignited on partial boundary. It leads that reactive waves interact with non-reactive ones, and they give birth to more shock, degenerate shock and rarefaction and their interactions. Then new complex structure occurs in burnt area.In Chapter6we investigate a class of n-dimensional combustion model with general initial discontinuity, even including closed initial discontinuity. We find that sometimes strong deto-nations can become Chapman-Jouguet detonations in combustion process. In the final part we analyze and uncover how the reactant area shrinks in reaction process.