Public statement.
noncomputable def
AVenhance.Ingredients.ansatz
{β : ℝ}
(I : Ingredients β)
{Φ : ℕ → ℝ → Homogenization.Vec 2 → ℝ}
(hΦ : IsStreamSeq I Φ)
(m : ℕ)
(κm : ℝ)
(Tm1 : ℝ → Homogenization.Vec 2 → ℝ)
(t : ℝ)
(x : Homogenization.Vec 2)
:
The multiscale ansatz θTilde_m, e.ansatz (4355), SECOND line — the object the source's
proof actually uses (e.tbm1.one, e.timecomp.0, §5.3); the ansatz is line 2,
with the large-scale flow index l_k throughout (and ΧTilde_{m,k} built from X⁻¹_{m-1,l_k}):
θTilde_m = T_{m-1} + ∑_{k∈ℤ} ξ_{m,k} ΧTilde_{m,k} · (∇(T_{m-1}∘X_{m-1,l_k})∘X⁻¹_{m-1,l_k}) + HTilde_m.
The tsum is finitely supported for each (t,x) (FILE 11), no junk.
Equations
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