On an integral equation in kinetic theory of gases
The authors investigate some convolution type integral equation on a finite interval with a completely monotone kernel arising at the kinetic theory of gases. Such equations have the form \[ f(x)= T_0(x)+\int_0^r T_{-1}(| x-t|)f(t) dt , \qquad t>0 \] where \[ T_n(x)=\frac{1}{\sqrt \pi}\int_0^\infty \exp(-s^2)\exp \left(-\frac{x}{s} \right) s^n ds,\qquad n=-1,0,1,\dots \] Using the connection with the Wiener-Hopf equation on the half-line they give a method for the construction of an approximate solution.
scientific article; zbMATH DE number 1131846