Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations

DÜZGÜN, FATMA; Mosconi, Sunra; Vespri, Vincenzo

doi:10.1007/s00028-019-00493-w

Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations

DÜZGÜN F. G., Mosconi S., Vespri V.

JOURNAL OF EVOLUTION EQUATIONS, cilt.19, sa.3, ss.845-882, 2019 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 19 Sayı: 3
Basım Tarihi: 2019
Doi Numarası: 10.1007/s00028-019-00493-w
Dergi Adı: JOURNAL OF EVOLUTION EQUATIONS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.845-882
Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
Hacettepe Üniversitesi Adresli: Evet

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.