Existence of front solutions for a nonlocal transport problem describing gas ionization

Matthias Günther, G. Prokert

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Abstract

We discuss a moving boundary problem arising from a model of gas ionization in the case of negligible electron diffusion and suitable initial data. It describes the time evolution of an ionization front. Mathematically, it can be considered as a system of transport equations with different characteristics for positive and negative charge densities. We show that only advancing fronts are possible and prove short-time well-posedness of the problem in Hölder spaces of functions. Technically, the proof is based on a fixed point argument for a Volterra type system of integral equations involving potential operators. It crucially relies on estimates of such operators with respect to variable domains in weighted Hölder spaces and related calculus estimates.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages24
Publication statusPublished - 2009

Publication series

NameCASA-report
Volume0930
ISSN (Print)0926-4507

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