On Boundary Null Controllability of Strongly Degenerate Hyperbolic Systems on Star-Shaped Planar Network

Abstract

In this paper we discuss the problem of boundary exact null controllability for weakly and strongly degenerate linear wave equation defined on star-shaped planar network. The network is represented by a singular measure in a bounded planar domain. The novelty of this article lies in the degeneration of the leading coefficient representative of the material properties at the common node of network. We discuss the existence of weak and strong solutions to the degenerate hyperbolic problem and establish the corresponding controllability properties.

Keywords

• degenerate hyperbolic equation
• weighted sobolev spaces, planar network
• singular measures
• boundary controllability