Summary
The Cahn-Hilliard model for phase separation in a binary alloy leads to the equations (I) ut=Δw, (II) w=ψ′ (u)− γΔu with an associated energy functional F(u)=f [ψ(u)+ +γ¦∇u¦2/2] dx. In this paper we discuss the existence theory for initial bounday value problems arising from modifications to the Cahn-Hilliard model due to the addition of the non-differentiable term α¦∇u¦dx to the energy F(u).
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Elliott, C.M., Mikelić, A. Existence for the Cahn-Hilliard phase separation model with a nondifferentiable energy. Annali di Matematica pura ed applicata 158, 181–203 (1991). https://doi.org/10.1007/BF01759304
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DOI: https://doi.org/10.1007/BF01759304