Global Cauchy problem for Kirchhoff equations

We consider the global Cauchy problem for generalized Kirchhoff equations. Under conditions upon the nonlinear part or upon the size of data, we show existence of a solution which is twice differentiable with respect to time and uniformly analytic with respect to spatial variables. When the nonlinear part does not depend of spatial variables, we give asymptotic estimates for lifespan of the solution and we prove the stability of the problem. (C) Academie des Sciences/Elsevier, Paris.