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We consider an infinite system of quasilinear first-order partialdifferential equations, generalized to contain spacial integration, whichdescribes an incompressible fluid mixture of infinite components in a linesegment whose motion is driven by unbounded and space-time dependentevaporation rates. We prove unique existence of the solution to theinitial-boundary value problem, with conservation-of-fluid condition at theboundary. The proof uses a map on the space of collection of characteristics,and a representation based on a non-Markovian point process withlast-arrival-time dependent intensity.

Point process with last-arrival-time dependent intensity and 1-dimensional incompressible fluid system with evaporation