Spatial Border-2 Transfer Theorems for Bounded Liquid-Vapor Transport

Evaporation models become useful for desert-water, porous-media, and collection problems only after the vapor-side pathway is stated with the same care as the evaporating surface. This paper develops Spatial Border-2 as a bounded vapor-side transfer layer. Border 1 supplies an interfacial source flux inherited from the companion bounded Robin-regime formulation; Border 2 records the receiving-side environment, sink, collector, pore channel, or outlet through which released vapor is transported. The main result is a stability theorem for the coupled Border1/Border-2 parabolic transfer problem. In a declared bounded regime, differences in vapor-side observations are controlled by the Border-1 input debit, Border-2 sink or collector-law debit, coefficient perturbations, interior residuals, numerical residuals, and observation uncertainty. A one-dimensional slab/pore worked regime shows how Péclet, Border-1 supply, Border-2 Biot, and collection Damkohler-type coordinates enter a concrete debit ledger. The contribution is not a universal desert-yield law. It is a reviewable mathematical layer that converts post-surface vapor motion into a bounded transfer claim with explicit hypotheses, residual channels, and evidence levels.