Global well-posedness of the Kirchhoff equation and Kirchhoff systems
  This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems. 
Tokio Matsuyama and Michael Ruzhansky
math.AP