Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Asymptotic stability of singular solution to nonlinear heat equation

Pages: 991 - 1001, Volume 25, Issue 3, November 2009      doi:10.3934/dcds.2009.25.991

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Dominika Pilarczyk - Instytut Matematyczny, Uniwersytet Wroclawski, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland (email)

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.

Keywords:  semilinear parabolic equation, asymptotics of solutions, supercritical nonlinearity.
Mathematics Subject Classification:  Primary: 35K57; Secondary: 35B33, 35B40.

Received: December 2008;      Revised: June 2009;      Published: August 2009.