Asymptotic stability of singular solution to nonlinear heat equation

Dominika Pilarczyk

doi:10.3934/dcds.2009.25.991

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2009, Volume 25, Issue 3: 991-1001. Doi: 10.3934/dcds.2009.25.991

This issue Previous Article Entropy range problems and actions of locally normal groups Next Article On the boundedness of solutions of the equation $u''+(1+f(t))u=0$

Asymptotic stability of singular solution to nonlinear heat equation

Dominika Pilarczyk^1,

1.
Instytut Matematyczny, Uniwersytet Wroclawski, pl. Grunwaldzki 2/4, 50-384 Wroclaw

Received: November 30, 2008

Revised: May 31, 2009

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K57; Secondary: 35B33, 35B40.

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