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On Critical Exponents for the Heat Equation with a Mixed Nonlinear Dirichlet–Neumann Boundary Condition

✍ Scribed by Bei Hu; Hong-Ming Yin

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
310 KB
Volume
209
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we consider the heat equation u s ⌬ u in an unbounded domain t N Ž . ⍀;R with a partly Dirichlet condition u x, t s 0 and a partly Neumann condition u s u p on the boundary, where p ) 1 and is the exterior unit normal on the boundary. It is shown that for a sectorial domain in R 2 and an orthant N Ž . domain in R there exists an explicit critical exponent p ⍀ ) 1 such that all c Ž x positive solutions blow up in finite time when p g 1, p while there exist c positive global solutions if p ) p and initial data are suitably small. All our c blowup results include the critical case.

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