Date of Graduation
Eberly College of Arts and Sciences
We study a stabilized Kuramoto-Sivanshinsky system in two-dimensional space. A model consists of a mixed Kuramoto-Sivanshinsky-Korteweg-de Vires equation, linearly coupled to an extra linear dissipative equation. The model is proposed to describe the surface waves on multi-layered liquid films. In this work, we investigate the stability of the solution to this system by establishing a priori energy estimate for the linearized problem of this non-linear system. We use linear iteration to prove the local existence of the solution to this system. Based on a weak global priori energy estimate, we further prove the global existence and uniqueness of classical solution for this system.
Cai, Maomao, "Solutions for 2-dimensional stabilized Kuramoto -Sivashinsky system" (2008). Graduate Theses, Dissertations, and Problem Reports. 4359.