The wave equation for the $p$-Laplacian

Michael DREHER

doi:10.14492/hokmj/1285766660

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Home > Journals > Hokkaido Math. J. > Volume 36 > Issue 1 > Article

February 2007 The wave equation for the $p$-Laplacian

Michael DREHER

Hokkaido Math. J. 36(1): 21-52 (February 2007). DOI: 10.14492/hokmj/1285766660

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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.