The steady states of the one-dimensional Cahn-hilliard equation

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Abstract

The steady states of the Cahn-Hilliard equation are studied as a function of interval length L and average mass m. We count the number of non-trivial monotone increasing steady state solutions and demonstrate that if m lies within the spinodal region then for almost every L∈(0, π{plus 45 degree rule}2√1-3m2), there are an even number of such solutions, and for L∈(π{plus 45 degree rule}2√1-3m2, ∞), there are an odd number of such solutions. If m lies within the metastable region, then for almost every L > 0 there are an odd number of solutions. © 1992.

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Novick-Cohen, A., & Peletier, L. A. (1992). The steady states of the one-dimensional Cahn-hilliard equation. Applied Mathematics Letters, 5(3), 45–46. https://doi.org/10.1016/0893-9659(92)90036-9

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