Null Controllability of Some Degenerate Wave Equations

摘要

This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations.through a boundary controller.First,the well-poseduess of linear degenerate wave equations is discussed.Then the null controllability of some degenerate wave equations is established,when a control acts on the non-degenerate boundary.Different from the known controllability results in the case that a control acts on the degenerate boundary,any initial value in state space is controllable in this case.Also,an explicit expression for the controllability time is given.Furthermore,a counterexample on the controllability is given for some other degenerate wave equations.