DCDS
Spectral analysis for transition front solutions in Cahn-Hilliard systems
Peter Howard Bongsuk Kwon
Discrete & Continuous Dynamical Systems - A 2012, 32(1): 125-166 doi: 10.3934/dcds.2012.32.125
We consider the spectrum associated with the linear operator obtained when a Cahn--Hilliard system on $\mathbb{R}$ is linearized about a transition wave solution. In many cases it's possible to show that the only non-negative eigenvalue is $\lambda = 0$, 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 structural conditions on our equations. More generally, we discuss and implement a straightforward numerical check of our condition, valid under mild structural conditions.
keywords: Evans function. transition fronts stability Cahn-Hilliard systems

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