Manuscript IX-C-ST@1 · IX-C-ST.tex · definition · 892f50c4

Definition: Supported developing presentation

The prescribed host and the supported laboratory · lines 294–326

IX-C-ST@1#def:support

Choose a product-adapted isometric developing embedding

ι : U = (- ϵ_{0}, H) \times B_{R} ⟶ M_{δ_{c}}, t = c_{light} (T - T_{Σ}),

with developed metric $η = diag (- 1, 1, 1, 1)$ . Choose

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

Observation tests belong to

T = D (V; C) .

For each such test $f$ , the whole truncated developed past

J_{η}^{-} (supp f) \cap {t \geq 0}

is included in $K_{*}$ . The compact laboratory contains a neighbourhood of $ι (K_{*})$ , and its closure is disjoint from $W$ .

The response has zero value and zero first $t$ -derivative at $t = 0$ . No additional incoming homogeneous or lateral boundary data are supplied. All compact test families have a positive smoothing margin inside the supported presentation.

Displayed formulas in this passage

unlabeled · line 297
$ι : U = (- ϵ_{0}, H) \times B_{R} ⟶ M_{δ_{c}}, t = c_{light} (T - T_{Σ}),$
unlabeled · line 304
$V = (0, T_{0}) \times B_{r_{0}}, R > r_{0} + T_{0}, K_{*} = [0, T_{0}] \times B_{r_{0} + T_{0}} ⋐ U .$
unlabeled · line 310
$T = D (V; C) .$
unlabeled · line 314
$J_{η}^{-} (supp f) \cap {t \geq 0}$

Definition: Supported developing presentation

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