Calculus of Variations and Partial Differential Equations

, Volume 42, Issue 1, pp 189–209

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

Authors

    • Department of Mathematics, Faculty of Education and Integrated Arts and SciencesWaseda University
Article

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

Abstract

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)

35B4035F3135D4037J5049L25

Copyright information

© Springer-Verlag 2010