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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The profile near blowup time for solution of the heat equation with a nonlinear boundary condition
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by Bei Hu and Hong-Ming Yin PDF
Trans. Amer. Math. Soc. 346 (1994), 117-135 Request permission

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
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 346 (1994), 117-135
  • MSC: Primary 35B40; Secondary 35B05, 35K60
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1270664-3
  • MathSciNet review: 1270664