Advances in Differential Equations

Very slow convergence to zero for a supercritical semilinear parabolic equation

Christian Stinner

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We study the asymptotic behavior of nonnegative solutions to the Cauchy problem for a semilinear parabolic equation with a supercritical nonlinearity. It is known that there are initial data such that the corresponding solution decays to zero with an algebraic rate. Furthermore, any algebraic rate which is slower than the self-similar rate occurs as decay rate for some solution. In this paper we prove that the convergence to zero can take place with an "arbitrarily" slow rate, if the initial data are chosen properly.

Article information

Adv. Differential Equations, Volume 14, Number 11/12 (2009), 1085-1106.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K15: Initial value problems for second-order parabolic equations 35B40: Asymptotic behavior of solutions 35K57: Reaction-diffusion equations


Stinner, Christian. Very slow convergence to zero for a supercritical semilinear parabolic equation. Adv. Differential Equations 14 (2009), no. 11/12, 1085--1106.

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