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On the convergence of a fourth order evolution equation to the Allen-Cahn equation |
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| Authors: | Georgia Karali Tonia Ricciardi |
| Institution: | a Department of Applied Mathematics, University of Crete, GR 71409, Heraklion, Greece b Institute for Applied and Computational Mathematics, FORTH, Crete, Greece c Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy |
| Abstract: | We construct special sequences of solutions to a fourth order nonlinear parabolic equation of Cahn-Hilliard/Allen-Cahn type, converging to the second order Allen-Cahn equation. We consider the evolution equation without boundary, as well as the stationary case on domains with Dirichlet boundary conditions. The proofs exploit the equivalence of the fourth order equation with a system of two second order elliptic equations with “good signs”. |
| Keywords: | Nonlinear parabolic equations Allen-Cahn Cahn-Hilliard equations |
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