Proceedings of the American Mathematical Society

Author(s): Qi S. Zhang; Z. Zhao
Journal: Proc. Amer. Math. Soc. 126 (1998), 1491-1500.
MSC (1991): Primary 35K57
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35K57

Qi S. Zhang
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: sz@math.missouri.edu

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ISSN 1088-6826 (e) ISSN 0002-9939 (p)

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