English

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

Analysis of PDEs 2025-01-14 v3

Abstract

We consider nonlinear hyperbolic systems with a general source and prove that for appropriately chosen smooth initial data the lifespan of the associated C1C^1-solution uu cannot be infinite. We employ ideas of F. John (1974) and L. H\"ormander (1987) to show that the derivative uxu_x of uu becomes unbounded in finite time.

Keywords

Cite

@article{arxiv.2204.12101,
  title  = {Formation of singularities in solutions to nonlinear hyperbolic systems with general sources},
  author = {Johannes Bärlin},
  journal= {arXiv preprint arXiv:2204.12101},
  year   = {2025}
}