Manuscript IX-A-ST@1 · IX-A-ST.tex · definition · 6e99d1b2

Definition: Supported developing presentation

Prescribed cone and a causally saturated developing laboratory › The local analytic contract · lines 307–330

IX-A-ST@1#def:support

Choose positive numbers $δ, T_{0}, r_{0}, R, H$ , with $R > r_{0} + T_{0}$ and $H > T_{0}$ , and an isometric developing identification of

U = (- δ, H) \times B_{R}

with a regular open region of $M_{μ}$ , whose compact subregions used below have closures disjoint from $W$ . Set

V = (0, T_{0}) \times B_{r_{0}}, Σ = {0} \times B_{R}, K_{*} = [0, T_{0}] \times B_{r_{0} + T_{0}} ⋐ U .

Observation and coordinate-source tests belong to $D (V) = C_{c}^{\infty} (V)$ , with the appropriate tensor indices.

The analytic prescription has zero homogeneous Cauchy data at $t = 0$ . All field dependence needed by these tests lies in $K_{*}$ . No undeclared lateral boundary data or incoming homogeneous solution is added.

Displayed formulas in this passage

unlabeled · line 312
$U = (- δ, H) \times B_{R}$
unlabeled · line 318
$V = (0, T_{0}) \times B_{r_{0}}, Σ = {0} \times B_{R}, K_{*} = [0, T_{0}] \times B_{r_{0} + T_{0}} ⋐ U .$

Definition: Supported developing presentation

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