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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Global solvability for the heat equation with boundary flux governed by nonlinear memory


Authors: Jeffrey R. Anderson, Keng Deng and Zhihua Dong
Journal: Quart. Appl. Math. 69 (2011), 759-770
MSC (2010): Primary 35B44, 35K05, 35K20
Published electronically: July 1, 2011
MathSciNet review: 2893999
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Abstract: We introduce the study of global existence and blowup in finite time for the heat equation with flux at the boundary governed by a nonlinear memory term. Via a simple transformation, the model may be written in a form which has been introduced in previous studies of tumor-induced angiogenesis. The present study is also in the spirit of extending work on models of the heat equation with local, nonlocal, and delay nonlinearities present in the boundary flux. Additionally, we provide a brief summary of related studies regarding heat equation models where memory terms are incorporated within reaction or diffusion.


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Additional Information

Jeffrey R. Anderson
Affiliation: College of Science, Technology, Engineering and Mathematics, University of Wisconsin-Stout, Menomonie, Wisconsin 54751
Email: andersonjeff@uwstout.edu

Keng Deng
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504
Email: deng@louisiana.edu

Zhihua Dong
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504
Email: zxd5200@louisiana.edu

DOI: http://dx.doi.org/10.1090/S0033-569X-2011-01238-X
PII: S 0033-569X(2011)01238-X
Keywords: Global existence, finite time blowup, memory boundary condition
Received by editor(s): April 28, 2010
Published electronically: July 1, 2011
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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