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Journal Articles Analysis and Applications Year : 2012

A sufficient condition for slow decay of a solution to a semilinear parabolic equation

Imen Ben Arbi
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Alain Haraux
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Abstract

We consider the equation psi t - Delta psi + c vertical bar psi vertical bar (p-1)psi = 0 with Neumann boundary conditions in a bounded smooth open connected domain of R-n with p > 1, c > 0. We show that if the initial condition is small enough and if the absolute value of its average overpasses a certain multiple of the pth power of its L-infinity norm, then psi(t, .) decreases like t(-1/(p-1)).

Dates and versions

hal-01448170 , version 1 (27-01-2017)

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Imen Ben Arbi, Alain Haraux. A sufficient condition for slow decay of a solution to a semilinear parabolic equation. Analysis and Applications, 2012, 10 (4), pp.363-371. ⟨10.1142/S0219530512500170⟩. ⟨hal-01448170⟩
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