We study a model of radiating gases that describes the interaction of an inviscid gas with photons. We show the existence of smooth traveling waves called ’shock profiles’, when the strength of the… (More)

We compute and justify rigorous geometric optics expansions for linear hyperbolic boundary value problems that do not satisfy the uniform Lopatinskii condition. We exhibit an amplification phenomenon… (More)

We construct global smooth solutions to the multidimensional isothermal Euler equations with a strong relaxation. When the relaxation time tends to zero, we show that the density converges towards… (More)

Assuming that a hyperbolic initial boundary value problem satsifies an a priori energy estimate with a loss of one tangential derivative, we show a well-posedness result in the sense of Hadamard. The… (More)

We consider a model for the interaction of a gas with photons. In the article [10], smooth traveling wave solutions called shock profiles have been constructed under a suitable smallness assumption… (More)

The aim of this paper is to investigate the linear stability of multidimensional shock waves that violate the uniform stability condition derived by A. Majda. Two examples of such shock waves are… (More)

The aim of these notes is to present some results on the stability of finite difference approximations of hyperbolic initial boundary value problems. We first recall some basic notions of stability… (More)

We develop a simple energy method for proving the stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems. In particular, we extend to several space… (More)

The well-posedness of hyperbolic initial boundary value problems is linked to the occurrence of zeros of the so-called Lopatinskii determinant. For an important class of problems, the Lopatinskii… (More)

We generalize the analysis of [12] and develop a singular pseudodifferential calculus. The symbols that we consider do not satisfy the standard decay with respect to the frequency variables. We thus… (More)