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Pattern formation with a conservation law. (English) Zbl 0960.35007
This paper considers pattern formation in systems with a conserved quantity by examining the amplitude equation. The conservation law gives rise to a large scale neutral mode, the effect of which must be included in the asymptotic analysis for pattern formation. The analysis shows that for certain parameter values all roll-type solutions are unstable. A new instability that differs from the Eckhaus instability is identified, with the property that it is amplitude driven and supercritical. Numerical simulations are given, and various applications are made, including convection with fixed-flux boundaries and convection in a magnetic field.

MSC:
35B32 Bifurcations in context of PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
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