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

Abstract

We consider nonlinear hyperbolic systems with a general source and prove that for appropriately chosen smooth initial data the lifespan of the associated $C^1$-solution $u$ cannot be infinite. We employ ideas of F. John (1974) and L. H\"ormander (1987) to show that the derivative $u_x$ of $u$ becomes unbounded in finite time.