| Abstract: |
| We prove convergence of a sequence of weak solutions to the nonlocal Cahn-Hilliard equation to the weak solution to the corresponding local Cahn-Hilliard equation. The analysis is done in the case of sufficiently smooth bounded domains with Neumann boundary condition and a $W^{1,1}$-kernel. The proof is based on an energy method.
Additionally, we prove the strong $L^p$-convergence of the nonlocal operator to a local differential operator together with a rate of convergence. The analysis also includes more singular kernels. |
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