Propagation of fronts in a nonlinear fourth order equation

By Paola Loreti, R. March. European journal of applied mathematics, 2000

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A new phase-field model for strongly anisotropic systems (2009, methodology): “In the electronic supplementary material, we use the method of matched asymptotic expansions (following Pego 1989; McFadden et al. 1993; Leo et al. 1998; Loreti & March 2000), which shows that the system (3.17)–(3.20) converges to anisotropic surface diffusion as e/0.”
On a Modified Conjecture of De Giorgi (2006, unknown): “Loreti and March considered in [LoMa00] the gradient ﬂows corresponding to the functionals F ε , F and proved the convergence as ε → 0 by formal asymptotic expansions.”
A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework (2014, background): “A formal description of a proof has been provided by March and Dozio [29] and a partial proof by Loreti and March [28].”