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September  2009, 25(3): 991-1001. doi: 10.3934/dcds.2009.25.991

Asymptotic stability of singular solution to nonlinear heat equation

Dominika Pilarczyk 1,

1. 

Instytut Matematyczny, Uniwersytet Wroclawski, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland

Received  December 2008 Revised  June 2009 Published  August 2009

In this paper, we discuss the asymptotic stability of singular steady states of the nonlinear heat equation $u_t=\Delta u+u^p$ in weighted $L^r$ - norms.
Keywords: semilinear parabolic equation, asymptotics of solutions, supercritical nonlinearity..
Mathematics Subject Classification: Primary: 35K57; Secondary: 35B33, 35B4.
Citation: Dominika Pilarczyk. Asymptotic stability of singular solution to nonlinear heat equation. Discrete & Continuous Dynamical Systems, 2009, 25 (3) : 991-1001. doi: 10.3934/dcds.2009.25.991
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