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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The profile near blowup time for solution of the heat equation with a nonlinear boundary condition


Authors: Bei Hu and Hong-Ming Yin
Journal: Trans. Amer. Math. Soc. 346 (1994), 117-135
MSC: Primary 35B40; Secondary 35B05, 35K60
MathSciNet review: 1270664
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Abstract: This paper studies the blowup profile near the blowup time for the heat equation $ {u_t} = \Delta u$ with the nonlinear boundary condition $ {u_n} = {u^p}$ on $ \partial \Omega \times [0,T)$. Under certain assumptions, the exact rate of the blowup is established. It is also proved that the blowup will not occur in the interior of the domain. The asymptotic behavior near the blowup point is also studied.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1270664-3
PII: S 0002-9947(1994)1270664-3
Keywords: Blowup rate, asymptotic behavior, elliptic estimates, parabolic estimates
Article copyright: © Copyright 1994 American Mathematical Society