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1 IF - Institut Fourier 2 MIP - Mathématiques pour l-Industrie et la Physique

Abstract : The large time behavior of non-negative solutions to the viscous Hamilton-Jacobi equation $\partial t u - \Delta u + | abla u|^q = 0$ is investigated for the critical exponent q=N+2-N+1. Convergence towards a rescaled self-similar solution to the linear heat equation is shown, the rescaling factor being $\ln{t}^{-N+1}$. The proof relies on the construction of a one-dimensional invariant manifold for a suitable truncation of the equation written in self-similar variables.





Autor: Thierry Gallay - Philippe Laurençot -

Fuente: https://hal.archives-ouvertes.fr/



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