Orateur
Description
We consider the one-dimensional diffusion approximation, non-equilibrium model of radiation hydrodynamics derived by Buet and Després (J. Quant. Spectrosc. Radiat. Transf. 85 (2004), no. 3-4, 385–418). This system describes a non-relativistic inviscid fluid subject to a radiative field under the non-equilibrium hypothesis, that is, when the temperature of the fluid is different from the radiation temperature, and it is a non-conservative parabolic balance law system. We are interested in the global existence and asymptotic behavior of small perturbation of constant equilibrium states. The approach we take can be divided into three steps: first, we study the local well-posedness of the system; second, the decay properties of the linear system around a constant state are studied under the framework of Sizhuta and Kawashima (Hokkaido Math. J. 14 (1985), no. 2, 249–275); and third, we perform the nonlinear energy estimate based on the linear results, which will give us the a priori energy estimate as well as the decay rate of solutions needed to conclude the global existence and asymptotic behavior. For this last step we introduce a notion of entropy for the system that allows us to recast it in a form such that the nonlinear estimate can be closed. This talk is based on a joint work with C. Lattanzio and R. G. Plaza.