Dynamic transition for Kuramoto-Sivashinsky equation and gas-liquid transition

In this dissertation we consider the dynamic transition of Kuramoto-Sivashinsky equation and gas-liquid transition. In addition, we study the pattern formation related to modified Kuramoto-Sivashinsky equation.;For the dynamic transition of Kuramoto-Sivashinsky equation, we consider the Neumann boundary condition and periodic boundary condition and unveil the type of transitions. We also study pattern formation related with the modified Kuramoto-Sivashinsky equation. We are interested in finding the nature of those patterns and we are able to explain some of them.;For the gas-liquid transition, we consider two different cases: the homogeneous and non-homogeneous cases. In both cases, we find the reduced equation to the center manifold which gives us the whole picture of the dynamics of our gas-liquid transition.