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- W2962858315 abstract "We consider the problem posed for $xin ℝ^N$ and $t>0$ with nonnegative and compactly supported initial data. We take the exponent $p>2$ which corresponds to slow $p$-Laplacian diffusion. The main feature of the paper is that the exponent $q$ takes the critical value $q=p-1$ which leads to interesting asymptotics. This is due to the fact that in this case both the Hamilton-Jacobi term $|nabla u|^q$ and the diffusive term $Delta_p u$ have a similar size for large times. The study performed in this paper shows that a delicate asymptotic equilibrium happens, so that the large-time behaviour of the solutions is described by a rescaled version of a suitable self-similar solution of the Hamilton-Jacobi equation $|nabla W|^{p-1}=W$, with logarithmic time corrections. The asymptotic rescaled profile is a kind of sandpile with a cusp on top, and it is independent of the space dimension." @default.
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- W2962858315 date "2011-01-01" @default.
- W2962858315 modified "2023-09-26" @default.
- W2962858315 title "Asymptotic behaviour of a nonlinear parabolic equation with gradient absorption and critical exponent" @default.
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- W2962858315 doi "https://doi.org/10.4171/ifb/258" @default.
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