The wave equation for the $p$-Laplacian.
Hokkaido Mathematical Journal, 36 (2007) pp.21-52
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.
|Uncontrolled Keywords||local in time Sobolev solutions, blow-up in finite time, weakly hyperbolic equations|