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

✍ Scribed by M. Günther; G. Prokert

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 285 KB
• Volume: 33
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1254

✦ Synopsis

Communicated by P. Colli

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.