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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Global asymptotic behavior of solutions
of a semilinear parabolic equation


Authors: Qi S. Zhang and Z. Zhao
Journal: Proc. Amer. Math. Soc. 126 (1998), 1491-1500
MSC (1991): Primary 35K57
MathSciNet review: 1458274
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the large time behavior of solutions for the semilinear parabolic equation $ \Delta u + Vu^{p} - u_{t} =0$. Under a general and natural condition on $V= V(x)$ and the initial value $u_{0}$, 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/S0002-9939-98-04525-0
PII: S 0002-9939(98)04525-0
Received by editor(s): November 6, 1996
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1998 American Mathematical Society