Outgassing and contamination: Strict solution of a Boltzman‐like model

Abstract

AbstractWe consider a Boltzmann‐like model of a problem of outgassing and contamination in a region ℛ. For simplicity, we assume that ℛ = ℛ1 ∪ ℛ2 ∪ ℛ3, where ℛ1 is the slab {x: −a < x < 0}, ℛ2 = {x:0 < x < b}, ℛ3 = {x: b < x < b1}. ℛ1 is the region where the contaminant particles are produced, ℛ2 is the ‘cavity’ where such particles migrate and interact with some inert gas, usually at low pressure, and ℛ3 is the region which is contaminated by the particles coming from ℛ2. In each of the three regions, the behaviour of the contaminant particles is represented by means of a Boltzmann‐like equation.We prove that such a mathematical problem has a unique positive strict solution, belonging to a suitable Banach space Y. A system of ordinary differential equations is also derived, which gives the global balances of the contaminant particles in each of the three regions.