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

Soohyun Bae

doi:10.3934/dcds.2010.26.823

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2010, Volume 26, Issue 3: 823-837. Doi: 10.3934/dcds.2010.26.823

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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

Received: December 31, 2008

Revised: September 30, 2009

Published: August 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K58, 35J61; Secondary: 35B35.

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

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