BLOW-UP IN A SUBDIFFUSIVE MEDIUM WITH ADVECTION

被引：5

作者：

Olmstead, W. Edward ^{[1
]}

Kirk, Colleen M. ^{[2
]}

Roberts, Catherine A. ^{[3
]}

机构：

[1] Northwestern Univ, Evanston, IL 60208 USA

[2] Calif Polytech State Univ San Luis Obispo, San Luis Obispo, CA 93407 USA

[3] Coll Holy Cross, Worcester, MA 01610 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 28卷 / 04期

关键词：

heat equation; subdiffusion; advection; blow-up; moving source; DIFFUSION;

D O I：

10.3934/dcds.2010.28.1655

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A mathematical model is presented for a localized energy source in a subdiffusive medium with advection. It is shown that blow-up cannot be prevented, regardless of the advection speed. This result holds for media associated with an unbounded spatial domain in one, two, or three dimensions. Results also suggest that increasing the advection speed will delay the time to blow-up, even though it does not prevent a blow-up. It is interesting to note that these results are in distinct contrast with the analogous classical diffusion problem, in which blow-up can be prevented by increasing sufficiently the advection speed. The asymptotic behavior of the temperature near the blow-up time is also presented.

引用

页码：1655 / 1667

页数：13

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