Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions


DOI: 10.1007/s00526-010-0385-4

Cite this article as:
Ishii, H. Calc. Var. (2011) 42: 189. doi:10.1007/s00526-010-0385-4


We study the long-time asymptotic behavior of solutions u of the Hamilton-Jacobi equation ut(x, t) + H(x, Du(x, t)) = 0 in Ω × (0, ∞), where Ω is a bounded open subset of \({\mathbb{R}^n}\), with Hamiltonian H = H(x, p) being convex and coercive in p, and establish the uniform convergence of u to an asymptotic solution as t → ∞.

Mathematics Subject Classification (2000)

35B40 35F31 35D40 37J50 49L25 

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Education and Integrated Arts and SciencesWaseda UniversityTokyoJapan

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