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Energy minimization using Sobolev gradients: application to phase separation and ordering. (English) Zbl 1097.49002

Summary: A common problem in physics and engineering is the calculation of the minima of energy functionals. The theory of Sobolev gradients provides an efficient method for seeking the critical points of such a functional. We apply the method to functionals describing coarse-grained Ginzburg–Landau models commonly used in pattern formation and ordering processes.

MSC:

49J10 Existence theories for free problems in two or more independent variables
65K10 Numerical optimization and variational techniques
74G15 Numerical approximation of solutions of equilibrium problems in solid mechanics
74G65 Energy minimization in equilibrium problems in solid mechanics
74N99 Phase transformations in solids
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References:

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