Optimal growth rates for a viscous Hamilton-Jacobi equation
type: Item
instance of: scholarly article
title: Optimal growth rates for a viscous Hamilton-Jacobi equation
zbMATH Open document ID: 1090.35036
author: Philippe Laurençot
author: Philippe Souplet
published in: Journal of Evolution Equations
publication date: 2006-03-09T00:00:00Z
review text: The large-time behavior of nonnegative solutions to the Cauchy problem for a viscous Hamilton-Jacobi equation with nonnegative initial data decaying at infinity is investigated. Namely, it is established that the function \(t\to t^{-N/m} | u(t)| _m\) (\(| u(t)| _m\) is the \(L_m\)-norm of the solution \(u(t)\)) is bounded from above and from below by positive real numbers. This result indicates an asymptotic behavior dominated by the hyperbolic part of the considered equation. Some estimates of the change of the value \(\Delta \ln u(t)\) are also established.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 5010079
zbMATH Keywords: Viscous Hamilton-Jacobi equation
zbMATH Keywords: Asymptotic behavior of solutions
zbMATH Keywords: large-time behavior
MaRDI profile type: Publication
full work available at URL: s00028-004-0181-8
OpenAlex ID: W2082136735
DOI: 10.1007/S00028-004-0181-8
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description: scientific article; zbMATH DE number 5010079