On a semilinear parabolic equation

Riahi, Lotfi

doi:10.1090/S0002-9939-06-08730-2

On a semilinear parabolic equation
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Proc. Amer. Math. Soc. 135 (2007), 59-68 Request permission

Abstract:

We introduce a general class of potentials $V=V(x,t)$ so that the semilinear parabolic equation $a\Delta u-\frac \partial {\partial t} u+ V u^p =0$ in $\mathbb {R}^n\times \ ]0,\infty [, n\geq 3, p>1$, $a>0$, has global positive continuous solutions. These results extend the recent ones proved by Zhang to a more general class of potentials.

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