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
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
收藏
页码:845 / 882
页数:38
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