JournalspmVol. 69, No. 1pp. 23–39

Rate of decay to 0 of the solutions to a nonlinear parabolic equation

  • Imen Ben Arbi

    Université Pierre et Marie Curie (Paris VI), France
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Abstract

We study the decay rate to 00 as t+t\rightarrow + \infty of the solution of the equation ψtΔψ+ψp1ψ=0\psi_t-\Delta\psi + | \psi |^{p-1} \psi=0 with Neumann boundary conditions in a bounded smooth open connected domain of Rn\mathbb{R}^{n} where p>1p>1. We show that either ψ(t,)\psi(t,\cdot) converges to 00 exponentially fast or ψ(t,)\psi(t,\cdot) decreases like t1(p1)t^{-\frac{1}{(p-1)}}.

Cite this article

Imen Ben Arbi, Rate of decay to 0 of the solutions to a nonlinear parabolic equation. Port. Math. 69 (2012), no. 1, pp. 23–39

DOI 10.4171/PM/1903