| import OAI.MathematicalPhysics.Transonic.Shooting.FiniteProfile | |
| import OAI.MathematicalPhysics.Transonic.Shooting.MatchedExistence | |
| namespace OAI | |
| namespace SepticProfile.SonicShooting | |
| open Set SourceFamily AxisBarriers | |
| open scoped ContDiff | |
| /-- A selected-parameter finite transonic source profile. -/ | |
| theorem exists_finite_transonic : ∃ (p : Parameter) (w : ℝ) (u : ℝ → ℝ), | |
| 0<w ∧ ContDiffOn ℝ ∞ u (Icc 0 (1+w)) ∧ | |
| (∀ z ∈ Icc (0:ℝ) (1+w), D (sig p) z (u z)*deriv u z=N (kap p) z (u z)) ∧ | |
| (∀ z ∈ Ioo (0:ℝ) 1, u z ∈ Ioo (0:ℝ) 1) ∧ | |
| (∀ z ∈ Ioc (0:ℝ) (1+w), u z=1 ↔ z=1) ∧ 0<deriv u 1 := by | |
| obtain ⟨M⟩ := exists_matched_pair | |
| exact ⟨M.parameter,M.sonic.width,M.localProfile,M.sonic.width_pos, | |
| fun z hz => (M.local_smooth_at hz).contDiffWithinAt,fun _ hz => M.local_equation hz, | |
| fun _ hz => M.local_range hz,fun _ hz => M.local_unique_sonic hz,M.local_slope⟩ | |
| end SepticProfile.SonicShooting | |
| end OAI | |