Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Global existence and blow-up for the fast diffusion equation with a memory boundary condition


Authors: Keng Deng and Qian Wang
Journal: Quart. Appl. Math. 74 (2016), 189-199
MSC (2010): Primary 35A01, 35B44, 35K59
DOI: https://doi.org/10.1090/qam/1425
Published electronically: December 7, 2015
MathSciNet review: 3472525
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study the long-time behavior of solutions to the fast diffusion equation with a memory boundary condition. The problem corresponds to a model introduced in previous studies of tumor-induced angiogenesis. We establish global existence and finite time blow-up results for the problem.


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Additional Information

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

Qian Wang
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Louisiana 70504
Email: qxw3519@louisiana.edu

DOI: https://doi.org/10.1090/qam/1425
Keywords: Fast diffusion equation, global existence, finite time blow-up, memory boundary condition.
Received by editor(s): November 12, 2014
Published electronically: December 7, 2015
Article copyright: © Copyright 2015 Brown University


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