From vlasov equation to degenerate nonlocal cahn-hilliard equation

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SUMMARY

    (10) Rd Combined with, this flux equation allows the authors to identify the limit of Jε and to prove that as ε, α → 0, the macroscopic densities tend to a solution of a degenerate nonlocal Cahn-Hilliard equation type. The authors can extract a subsequence (not relabelled) such that p ε → in L t L 1x strongly for 1 ≤ p and amp;lt; ∞ where solves in the distributional sense the equation ∂t - div( ∇ )=0, with initial data 0=Rd f 0 (x, ξ ) dξ. =-δ. Rd ( f ε (t, x, ξ )(1 - ψn (ξ )) dξ L 1t,x ≤ |ξ |≥n f ε (t, x . . .

     

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