Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations


DÜZGÜN F. G. , Mosconi S., Vespri V.

JOURNAL OF EVOLUTION EQUATIONS, cilt.19, ss.845-882, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 19 Konu: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s00028-019-00493-w
  • Dergi Adı: JOURNAL OF EVOLUTION EQUATIONS
  • Sayfa Sayıları: ss.845-882

Özet

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.