Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations

被引：19

作者：

Duzgun, Fatma Gamze ^{[1
]}

Mosconi, Sunra ^{[2
]}

Vespri, Vincenzo ^{[3
]}

机构：

[1] Hacettepe Univ, Dept Math, TR-06800 Ankara, Turkey

[2] Univ Catania, Dipartimento Matemat & Informat, Viale A Doria 6, I-95125 Catania, Italy

[3] Univ Firenze, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2019年 / 19卷 / 03期

关键词：

Anisotropic equations; Finite speed of propagation; L-infinity-estimates; Non-uniqueness; POROUS-MEDIUM EQUATION; SELF-SIMILAR SOLUTIONS; LOCAL BOUNDEDNESS; INITIAL TRACES; CAUCHY-PROBLEM; REGULARITY;

D O I：

10.1007/s00028-019-00493-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：845 / 882

页数：38

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