Stability of geometric blowup
The author continues in this paper his program of studying models of singularity formation for quasilinear first-order hyperbolic systems. Solutions are obtained in domains of the form \(\{t<T\}\), and blow up at exactly one point on \(\{t=T\}\). The main assumption is that blow-up occurs along one simple, genuinely nonlinear, characteristic direction. This is a continuation of the author's earlier work, in which analyticity assumptions are removed in the spirit of his paper [Commun. Partial Differ. Equations 21, No. 5-6, 923-969 (1996; Zbl 0858.35082)]. As in these works, the blow-up surface remains out of reach because of the lack of good hyperbolicity properties of the ``blow-up system''.
quasilinear first-order hyperbolic systems
scientific article; zbMATH DE number 1419577