Global asymptotic behavior of solutions of a semilinear parabolic equation
Authors:
Qi S. Zhang and Z. Zhao
Journal:
Proc. Amer. Math. Soc. 126 (1998), 14911500
MSC (1991):
Primary 35K57
MathSciNet review:
1458274
Fulltext PDF Free Access
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Abstract: We study the large time behavior of solutions for the semilinear parabolic equation . Under a general and natural condition on and the initial value , we show that global positive solutions of the parabolic equation converge pointwise to positive solutions of the corresponding elliptic equation. As a corollary of this, we recapture the global existence results on semilinear elliptic equations obtained by Kenig and Ni and by F.H. Lin and Z. Zhao. Our method depends on newly found global bounds for fundamental solutions of certain linear parabolic equations.
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Additional Information
Qi S. Zhang
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email:
sz@math.missouri.edu
Z. Zhao
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email:
zzhao@math.missouri.edu
DOI:
http://dx.doi.org/10.1090/S0002993998045250
PII:
S 00029939(98)045250
Received by editor(s):
November 6, 1996
Communicated by:
Jeffrey B. Rauch
Article copyright:
© Copyright 1998
American Mathematical Society
