Singular perturbation models in phase transitions for second-order materials
The authors use the \(\Gamma\)-convergence technique to characterize the singular perturbation limit of a family of rescaled energies \(F(u,\Omega)\) for dimensions \(n>1\) (the analysis for \(n=1\) was obtained by other authors). Here \(u\) represents the energy and \(\Omega\) is a bounded domain. The limiting functional \(F\) provides the effective energy on the phase transition surface.NEWLINENEWLINE The onset of pattern formation in the two component bilinear membranes and amphiphilic monolayers leads to the analysis of the energy \(u\) which includes the stiffness coefficient (\(-q\)). Authors found that curvature instabilities and pattern formation will occur when (\(-q\)) is negative. Compactness results are obtained in addition to an integral representation of the limit energy.
scientific article; zbMATH DE number 6054376