Spectral analysis for transition front solutions in Cahn-Hilliard systems | Zendy

Peter Howard | Zendy; Bongsuk Kwon | Zendy

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Spectral analysis for transition front solutions in Cahn-Hilliard systems

Author(s) -

Peter Howard,

Bongsuk Kwon

Publication year - 2011

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2012.32.125

Subject(s) - eigenvalues and eigenvectors , stability (learning theory) , cahn–hilliard equation , function (biology) , mathematics , spectrum (functional analysis) , front (military) , transition (genetics) , mathematical analysis , mathematical physics , physics , pure mathematics , computer science , quantum mechanics , partial differential equation , biochemistry , chemistry , gene , evolutionary biology , meteorology , biology , machine learning

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 conditionsclose3

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