Cercignani, Carlo A first approach to solutions for the steady nonlinear Boltzmann equation. (English) Zbl 0944.76078 Maiellaro, Michele (ed.) et al., The proceedings of the 9th international conference on Waves and stability in continuous media, Bari, Italy, October 6-11, 1997. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 57, 121-131 (1998). Summary: We discuss the Boltzmann equation in a slab, with boundary conditions of diffuse reflection and mass conservation at the wall, and assigned total mass (per unit area). We prove that there is at least one non-negative measure-valued solution. The physical model is provided by Maxwellian molecules with angular cutoff. The equation is rewritten after a change of variables which is shown to be invertible.For the entire collection see [Zbl 0912.00027]. MSC: 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 45K05 Integro-partial differential equations Keywords:existence of solution; one-dimensional nonlinear Boltzmann equation; slab; diffuse reflection; mass conservation; non-negative measure-valued solutions; Maxwellian molecules; angular cutoff; change of variables PDFBibTeX XMLCite \textit{C. Cercignani}, in: The proceedings of the 9th international conference on Waves and stability in continuous media, Bari, Italy, October 6--11, 1997. Palermo: Circolo Matematico di Palermo. 121--131 (1998; Zbl 0944.76078)