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.

Name | CASA-report |
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Volume | 0930 |
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ISSN (Print) | 0926-4507 |
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