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

DOI:
https://doi.org/10.1090/S0002-9939-98-04525-0

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 . 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:
https://doi.org/10.1090/S0002-9939-98-04525-0

Received by editor(s):
November 6, 1996

Communicated by:
Jeffrey B. Rauch

Article copyright:
© Copyright 1998
American Mathematical Society