# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 36 (2007) pp.21-52

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### Abstract

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.

MSC(Primary) 35L80 35L70 local in time Sobolev solutions, blow-up in finite time, weakly hyperbolic equations