Propagation of analyticity for a class of nonlinear hyperbolic equations

2010/12/17 by Sergio Spagnolo, Spagnolo, Sergio
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1012.3949

15 pages

arxiv created 2010/12/17 · arxiv updated 2010/12/20

Abstract

The propagation of analyticity for a solution u(t,x) to a nonlinear weakly hyperbolic equation of order m, means that if u, and its time derivatives up to the order m-1, are analytic in the space variables x at the initial time, then they remain analytic for any time. Here we prove that such a property holds for the solutions bounded in C-infinity of a special class of homogeneous equations in one space variable, with time dependent coefficient.

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