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September  2010, 26(3): 823-837. doi: 10.3934/dcds.2010.26.823

Weighted $L^\infty$ stability of positive steady states of a semilinear heat equation in $\R^n$

Soohyun Bae 1,

1. 

Faculty of Liberal Arts and Sciences, Hanbat National University, Daejeon, 305-719, South Korea

Received  January 2009 Revised  October 2009 Published  December 2009

This paper deals with the stability of steady states of the semilinear heat equation $u_t=$Δ$u+K(x)u^p+f(x)$ under proper assumptions on $K(x)$ and $f(x)$. We prove the weak asymptotic stability of positive steady states with respect to weighted uniform norms.
Keywords: stability, Semilinear heat equations, weak asymptotic stability., positive steady states.
Mathematics Subject Classification: Primary: 35K58, 35J61; Secondary: 35B3.
Citation: Soohyun Bae. Weighted $L^\infty$ stability of positive steady states of a semilinear heat equation in $\R^n$. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 823-837. doi: 10.3934/dcds.2010.26.823
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