A Note on the Asymptotic Behavior of Parabolic Monge‐Ampère Equations on Riemannian Manifolds

Qiang Ru

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: We study the asymptotic behavior of the parabolic Monge‐Ampère equation ∂φ(x, t)/∂t = log (det(g(x) + Hessφ(x, t))/detg(x)) − λφ(x, t) in 𝕄 × (0, ∞), φ(x, 0) = φ0(x) in 𝕄, where 𝕄 is a compact complete Riemannian manifold, λ is a positive real parameter, and φ0(x) : 𝕄 → ℝ is a smooth function. We show a meaningful asymptotic result which is more general than those in Huisken, 1997.

Date: 2013
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https://doi.org/10.1155/2013/304864

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:304864

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