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

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Abstract

We consider an infinite system of quasilinear first-order partial differential equations, generalized to contain spacial integration, which describes an incompressible fluid mixture of infinite components in a line segment whose motion is driven by unbounded and space-time dependent evaporation rates. We prove unique existence of the solution to the initial-boundary value problem, with conservation-of-fluid condition at the boundary. The proof uses a map on the space of collection of characteristics, and a representation based on a non-Markovian point process with last-arrival-time dependent intensity.

Original languageEnglish
Pages (from-to)171-212
Number of pages42
JournalFunkcialaj Ekvacioj
Volume60
Issue number2
DOIs
Publication statusPublished - 2017

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Keywords

  • Characteristic curves
  • Non-Markov point process
  • Partial differential integral equations
  • Quasilinear first-order infinite system

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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