\`x^2+y_1+z_12^34\`
Advanced Search
Advanced Search
Advanced Search
This issue Previous Article Next Article
Article Contents
Article Contents
2010, Volume 28, Issue 4: 1655-1667. Doi: 10.3934/dcds.2010.28.1655
This issue Previous Article Local well-posedness in low regularity of the MKDV equation with periodic boundary condition Next Article Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

Blow-up in a subdiffusive medium with advection

  • 1.

    Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208

  • 2.

    Mathematics, California Polytechnic State University, San Luis Obispo, CA 93407

  • 3.

    Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610

Received:  September 30, 2009
Revised:  January 31, 2010
Published:  November 2010
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 35K60, 45D05, 80A20.

    Citation:
    shu

    \begin{equation} \\ \end{equation}
    • Related Papers
  • Cited by
  • Access History
  • 加载中
PDF
XML
Export Citation
SHARE
Email to a Friend

Article Metrics

HTML views() PDF downloads(119) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return
    Site map Copyright © 2022 American Institute of Mathematical Sciences