On the well-posedness of the hyperelastic rod equation

Hasan Inci

On the well-posedness of the hyperelastic rod equation

Analysis of PDEs 2016-11-07 v1

Authors: Hasan Inci

Abstract

In this paper we consider the hyperelastic rod equation on the Sobolev spaces $H^s(\R)$ , $s > 3/2$ . Using a geometric approach we show that for any $T > 0$ the corresponding solution map, $u(0) \mapsto u(T)$ , is nowhere locally uniformly continuous. The method applies also to the periodic case $H^s(\mathbb T)$ , $s > 3/2$ .

Keywords

hyperelastic rod equation Sobolev spaces well-posedness solution map local uniform continuity geometric approach periodic case

Cite

@article{arxiv.1611.01188,
  title  = {On the well-posedness of the hyperelastic rod equation},
  author = {Hasan Inci},
  journal= {arXiv preprint arXiv:1611.01188},
  year   = {2016}
}

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