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A Note on a Question of Blow-Up for Semilinear Parabolic Equations

โœ Scribed by Mingxin Wang; Qin Zhang

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
138 KB
Volume
198
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

This paper studies the problem ยจs dยจq ยจq y 1 y cos x ยจp , for 0x -1 and t ) 0, ลฝ .

for x s 0, 1 and t ) 0,

x ยจx, 0 s ยจx , for 0x -1,

ลฝ . ลฝ .

0 where 1qp, d ) 0. It is shown that for large initial data if p -2 q y 1 or p s 2q y 1 but d is small, then the positive solution blows up in finite time. It is also proved that the positive solution is bounded from above for all time if ' ' ลฝ . ลฝ . p) 2q 2 qy 1q 2 . Finally, the blow-up set is studied.

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