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- W2019507366 abstract "On a compact Riemannian manifold (M,g), we consider the existence and nonexistence of global solutions for the parabolic Monge–Ampère equation(⁎){∂∂tφ=log(det(g+Hessφ)detg)−λφp−f(x),φ(x,0)=φ0(x). Here p>1 and λ are real parameters. −f,φ0:M→(0,+∞) are smooth functions on M. If λ>0, then the solution φ of (⁎) exists for all times t and φt=φ(⋅,t) converges exponentially towards a solution φ∞ of its stationary equation as t→∞. In the case of λ<0, it does not have the global solution of (⁎). Thus we obtain the nonexistence of the positive solution for the stationary equation of (⁎)." @default.
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- W2019507366 date "2012-05-01" @default.
- W2019507366 modified "2023-09-27" @default.
- W2019507366 title "Existence of the global solution for the parabolic Monge–Ampère equations on compact Riemannian manifolds" @default.
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- W2019507366 doi "https://doi.org/10.1016/j.jmaa.2011.12.005" @default.
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