In the following work, we consider Boltzmann equation that models a polyatomic gas by representing microscopic internal energy continuous variable I. Under some convenient assumptions on transition function $ \mathcal{B} $, prove linearized operator \mathcal{L} of this model is Fredholm operator. For this, write as perturbation collision frequency multiplication operator, and \mathcal{K} compac...

The invertibility of second-order finite-difference operators with constant operator coefficients acting in the Banach space two-sided vector sequences is proved under condition their uniform injectivity (in particular, left invertibility), or surjectivity right Fredholm property.

Abstract The problem of determining the domain closure Laplace-Beltrami operator on a 2D almost-Riemannian manifold is considered. Using tools from theory Lie groupoids natural domains perturbations are found. main novelty that presented method allows us to treat geometries with tangency points. This kind singularity difficult since those points do not have tubular neighbourhood compatible metr...