Formation of singularities in solutions to nonlinear hyperbolic systems with general sources

2022/04/26 by Bärlin, Johannes · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.12101

Abstract

We consider nonlinear hyperbolic systems with a general source and prove that for appropriately chosen smooth initial data the lifespan of the associated C¹-solution u cannot be infinite. We employ ideas of F. John (1974) and L. Hörmander (1987) to show that the derivative u_x of u becomes unbounded in finite time.

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