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

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Abstract

We study the long-time asymptotic behavior of solutions u of the Hamilton-Jacobi equation u t (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 → ∞.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education and Integrated Arts and Sciences, Waseda University, Nishi-Waseda, Shinjuku, Tokyo, 169-8050, Japan

    Hitoshi Ishii

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  1. Hitoshi Ishii
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Correspondence to Hitoshi Ishii.

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Communicated by L. Ambrosio.

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Ishii, H. Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions. Calc. Var. 42, 189–209 (2011). https://doi.org/10.1007/s00526-010-0385-4

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  • DOI: https://doi.org/10.1007/s00526-010-0385-4

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