Null Controllability of the Kuramoto-Sivashinsky Equation on star-shaped   trees
  In this paper we treat controllability properties for the linear Kuramoto-Sivashinsky equation on a network with two types of boundary conditions. More precisely, the equation is considered on a star-shaped tree with Dirichlet and Neumann boundary conditions. By using the moment theory we can derive null-controllability properties with boundary controls acting on the external vertices of the tree. In particular, the controllability holds if the anti-diffusion parameter of the involved equation does not belong to a critical countable set of real numbers. We point out that the critical set for which the null-controllability fails differs from the first model to the second one. 
Cristian M. Cazacu, Liviu I. Ignat, and Ademir F. Pazoto
math.OC math.AP