Ji, Xinhua; Chen, Dequan A representation of the solution of the Cauchy problem for a degenerate hyperbolic equation in several independent variables. (English) Zbl 0755.35074 Topics in mathematical analysis, Vol. Dedicated Mem. of A. L. Cauchy, Ser. Pure Math. 11, 456-477 (1989). Summary: [For the entire collection see Zbl 0721.00014.]We deal with a degenerate hyperbolic equation which is invariant under a transformation group. First, using a geometric method, we obtain the fundamental solution of this equation. Then by the Green integral formula we give the solution of its Cauchy problem explicitly. MSC: 35L80 Degenerate hyperbolic equations 35C15 Integral representations of solutions to PDEs 35A30 Geometric theory, characteristics, transformations in context of PDEs 35A08 Fundamental solutions to PDEs 35L15 Initial value problems for second-order hyperbolic equations 58J70 Invariance and symmetry properties for PDEs on manifolds Keywords:group invariance; transformation group; Green’s integral formula; Cauchy’s problem Biographic References: Cauchy, A. L. Citations:Zbl 0721.00014 PDFBibTeX XMLCite \textit{X. Ji} and \textit{D. Chen}, in: Analytic and Gevrey regularity for linear partial differential operators. . 456--477 (1989; Zbl 0755.35074)