SPECTRAL ANALYSIS FOR TRANSITION FRONT SOLUTIONS IN CAHN-HILLIARD SYSTEMS

Abstract

We consider the spectrum associated with the linear operator ob- tained when a Cahn{Hilliard system on ℝ is linearized about a transition wave solution. In many cases it's possible to show that the only non-negative ei- genvalue is λ = 0, and so stability depends entirely on the nature of this neutral eigenvalue. In such cases, we identify a stability condition based on an appropriate Evans function, and we verify this condition under strong struc- tural conditions on our equations. More generally, we discuss and implement a straightforward numerical check of our condition, valid under mild structural conditions