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Existence of front solutions for a nonlocal transport problem describing gas ionization
Author(s) -
Günther M.,
Prokert G.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1254
Subject(s) - mathematics , front (military) , ionization , gas dynamics , calculus (dental) , mathematical analysis , mechanics , physics , quantum mechanics , ion , meteorology , medicine , dentistry
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. Copyright © 2010 John Wiley & Sons, Ltd.