Asymptotic behavior for a viscous Hamilton-Jacobi equation with critical exponent

Simple item page
dc.creatorGallay, Thierry
dc.creatorLaurençot, Philippe
dc.date2006-09-27
dc.date.accessioned2026-07-07T07:25:17Z
dc.date.available2026-07-07T07:25:17Z
dc.descriptionThe large time behavior of non-negative solutions to the viscous Hamilton-Jacobi equation $u_t - Δu + |\nabla u|^q = 0$ in the whole space $R^N$ is investigated for the critical exponent $q = (N+2)/(N+1)$. Convergence towards a rescaled self-similar solution of the linear heat equation is shown, the rescaling factor being $(\log(t))^{-(N+1)}$. The proof relies on the construction of a one-dimensional invariant manifold for a suitable truncation of the equation written in self-similar variables.
dc.description17 pages, no figure
dc.identifierhttps://arxiv.org/abs/math/0609750
dc.identifierhttp://arxiv.org/abs/math/0609750
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116668
dc.subjectAnalysis of PDEs
dc.subject35B33; 35B40; 35K55; 37L25
dc.titleAsymptotic behavior for a viscous Hamilton-Jacobi equation with critical exponent
dc.typetext

Files

Collections

arXiv