Optimal lower bound of the grow-up rate for a supercritical parabolic equation

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

doi:10.1016/j.jde.2006.01.019

Optimal lower bound of the grow-up rate for a supercritical parabolic equation

Marek Fila, John R King + Show 2 more

https://doi.org/10.1016/j.jde.2006.01.019

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Journal: Journal of Differential Equations	Publication Date: Mar 9, 2006
Citations: 34	License type: elsevier-specific: oa user license

Affiliation: University of Nottingham, Tohoku University, RWTH Aachen University, Comenius University Bratislava

#Grow-up Rate #Decay Rate Of Initial Data + Show 8 more

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Abstract

We study the behavior of solutions of the Cauchy problem for a supercritical semilinear parabolic equation which approach a singular steady state from below as t → ∞ . It is known that the grow-up rate of such solutions depends on the spatial decay rate of initial data. We give an optimal lower bound on the grow-up rate by using a comparison technique based on a formal asymptotic analysis.

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