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# Communications in Mathematical Sciences

## Volume 18 (2020)

### Number 6

### Non-degenerate stationary solution for outﬂow problem on the 1-D viscous heat-conducting gas with radiation

Pages: 1661 – 1684

DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n6.a7

#### Authors

#### Abstract

This paper studies the asymptotic behavior of the solution to the initial boundary value problem of a one-dimensional compressible viscous heat-conducting gas with radiation. We consider an outflow problem, where the gas blows out the region through the boundary, of the general gases including ideal polytropic gas. First, we give the necessary and sufficient conditions for an existence of the non-degenerate stationary solution. In addition, using the energy method, it proves the asymptotic stability of the solutions under the assumption that the initial perturbation and the boundary data in the Sobolev space is small. We also demonstrate the convergence rate for the exponential and logarithmic decay of the solver. Note that it is the result of the outflow problem of the viscous heatconducting gas with radiation in the half line.

#### Keywords

compressible radiation hydrodynamics, outflow problem, stationary solution, stability, convergence rate

#### 2010 Mathematics Subject Classification

35B35, 35L65, 35Q30, 74J40, 76D33

Received 3 March 2020

Accepted 30 March 2020

Published 4 November 2020