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• W3105583710 abstract "We study the large-time behaviour of the solutions u of the evolution equation involving nonlinear diffusion and gradient absorption $$partial_t u - Delta_p u + vertnabla uvert^q = 0$$ We consider the problem posed for $$x in mathbb R^N $$ and t > 0 with non-negative and compactly supported initial data. We take the exponent p > 2 which corresponds to slow p-Laplacian diffusion, and the exponent q in the superlinear range 1 < q < p − 1. In this range the influence of the Hamilton–Jacobi term $$ vertnabla uvert^q$$ is determinant, and gives rise to the phenomenon of localization. The large-time behaviour is described in terms of a suitable self-similar solution that solves a Hamilton–Jacobi equation. The shape of the corresponding spatial pattern is rather conical instead of bell-shaped or parabolic." @default.
• W3105583710 created "2020-11-23" @default.
• W3105583710 creator A5002395669 @default.
• W3105583710 creator A5028901813 @default.
• W3105583710 date "2007-10-11" @default.
• W3105583710 modified "2023-09-30" @default.
• W3105583710 title "Localized Non-diffusive Asymptotic Patterns for Nonlinear Parabolic Equations with Gradient Absorption" @default.
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• W3105583710 doi "https://doi.org/10.1007/s10884-007-9093-y" @default.
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