Global Strong Solutions to the Cauchy Problem of One Dimensional Compressible Viscous Reactive Gas with Degenerate Heat Conductivity

This paper considers the Cauchy problem of the one dimensional compressible viscous reactive gas. For the case that the heat conductivity is proportional to a positive power of the temperature, the global existence of strong solutions with large initial data is established. In particular, it’s more difficult to derive the lower and upper bounds of both the density and temperature due to the degenerate heat conductivity.