  In this paper, we study a linear system related to the 2d system of Euler
equations with thermal conduction in the quasi-isobaric approximation of
Kull-Anisimov [14]. This model is used for the study of the ablation front
instability, which appears in the problem of inertial confinement fusion. This
physical system contains a mixing region, in which the density of the gaz
varies quickly, and one denotes by L0 an associated characteristic length. The
system of equations is linearized around a stationary solution, and each
perturbed quantity is written using the normal modes method. The resulting
linear system is not self-adjoint, of order 5, with coefficients depending on x
and on physical parameters $\alpha, \beta$. We calculate Evans function
associated with this linear system, using rigorous constructions of decreasing
at $\pm \infty$ solutions of systems of ODE. We prove that for $\alpha$ small,
there is no bounded solution of the linearized system.
