| Abstract: |
| We discuss pattern formation arising from combinations of Ginzburg-Landau and Swift-Hohenberg dynamics. Individually these are well-studied processes where the former involves separation into phases and the latter involves small scale stripes and dots. Such systems were proposed to generate new patterns by leveraging the competition between Ginzburg-Landau and Swift-Hohenberg dynamics, and were suggested for the development of new porous structures for material sciences. We present a three-species mixture described by a Cahn-Hilliard-Swift-Hohenberg system. Singular potentials are introduced to adhere to essential physical constraints, and well-posedness results will be reported. Numerical simulations demonstrate complex pattern formation as seen in pigment patterns of animals. If time permits, we discuss the numerical analysis of a positive preserving scheme for solving such Cahn-Hilliard-Swift-Hohenberg system with singular potentials. |
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