On the stability of semi-discrete shock profiles by means of an Evans function in infinite dimension

We are concerned with the spectral stability of semi-discrete shock profiles. This problem involves a retarded differential operator with variable coefficients. We construct a reduced Evans function, using the fact that the unstable manifold of the eigenvalue equations is finite dimensional - although the full eigenvalue equations are not. This enables us to derive a necessary condition for stability. (C) 1999 Academie des Sciences/Editions scientifiques et medicales Elsevier SAS.