Advances in Differential Equations

Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent

Marek Fila, John R. King, Michael Winkler, and Eiji Yanagida

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We consider the Cauchy problem for a semilinear parabolic equation with a nonlinearity which is critical in the Joseph-Lundgren sense. We find the grow-up rate of solutions that approach a singular steady state from below as $t\to\infty$. The grow-up rate in the critical case contains a logarithmic term which does not appear in the Joseph-Lundgren supercritical case, making the calculations more delicate.

Article information

Adv. Differential Equations, Volume 12, Number 1 (2007), 1-26.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B33: Critical exponents 35B40: Asymptotic behavior of solutions 35K15: Initial value problems for second-order parabolic equations


Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji. Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent. Adv. Differential Equations 12 (2007), no. 1, 1--26.

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