We consider generalized wave equations for the $p$--Laplacian and prove the local in time existence of solutions to the Cauchy problem. We give an estimate of the life-span of the solution, and show by a generic counter-example that global in time solutions can not be expected.
"The wave equation for the $p$-Laplacian." Hokkaido Math. J. 36 (1) 21 - 52, February 2007. https://doi.org/10.14492/hokmj/1285766660