Global solvability for Kirchhoff equation in special classes of non-analytic functions (Q855378)

This paper represents a generalization of \textit{R. Manfrin}'s results, see [J. Differ. Equations 211, No. 1, 38-60 (2005; Zbl 1079.35074)], devoted to solvability of the Cauchy problem for the Kirchhoff equation: \[ u_{tt}-a(t)\Delta u=0,\,(x,t)\in[0,T]\times \mathbb R^n; \] \[ u(0,x)=u_0(x),\,u_t(0,x)=u_1(x),\,x\in \mathbb R^n, \] where \[ a(t)=\sqrt{1+\int_{R^n}\mid \triangledown_x u(t,x)\mid^2}, \] in some special, called WKB, classes of functions.