On steady solutions to a model of chemically reacting heat conducting compressible mixture with slip boundary conditions

TL;DR

This paper studies steady solutions of a complex model describing chemically reacting, heat-conducting compressible mixtures, extending known results to new boundary conditions and parameter ranges.

Contribution

It establishes the existence of weak or variational entropy solutions under slip boundary conditions, broadening the understanding of such systems.

Findings

Existence of weak solutions for slip boundary conditions.

Extension of parameter ranges for solution existence.

Comparison with solutions under Dirichlet boundary conditions.

Abstract

We consider a model of chemically reacting heat conducting compressible mixture. We investigate the corresponding system of partial differential equations in the steady regime with slip boundary conditions for the velocity and, in dependence on the model parameters, we establish existence of either weak or variational entropy solutions. The results extend the range of parameters for which the existence of weak solutions is known in the case of homogeneous Dirichlet boundary conditions for the velocity.