Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations

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DÜZGÜN F. G., Mosconi S., Vespri V.

JOURNAL OF EVOLUTION EQUATIONS, vol.19, no.3, pp.845-882, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.1007/s00028-019-00493-w
  • Journal Name: JOURNAL OF EVOLUTION EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.845-882
  • Hacettepe University Affiliated: Yes

Abstract

We consider a quasilinear parabolic Cauchy problem with spatial anisotropy of orthotropic type and study the spatial localization of solutions. Assuming that the initial datum is localized with respect to a coordinate having slow diffusion rate, we bound the corresponding directional velocity of the support along the flow. The expansion rate is shown to be optimal for large times.