Stability of solution for uncertain wave equation

Abstract

The uncertain wave equation is an important type of uncertain partial differential equation driven by Liu process which is a special type of uncertain process with independent and stationary increments. For an uncertain wave equation, it is head for us to get its solution. What is more, even if we get it, we still should to know whether the obtained solution is stable or not. So this paper puts forward the concept of stability of uncertain wave equations in the sense of convergence in uncertain measure. Then we discuss the condition for an uncertain wave equation being stable and prove the stability theorem. In addition, some examples are given to show what is the concept of stability exactly and how to judge an uncertain wave equation being stable.