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Local asymptotics for nonlocal convective Cahn-Hilliard equations with W<sup>1,1</sup> kernel and singular potential

Local asymptotics for nonlocal convective Cahn-Hilliard equations with W1,1 kernel and singular potential

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DAVOLI, Elisa, Luca SCARPA, Lara TRUSSARDI, 2021. Local asymptotics for nonlocal convective Cahn-Hilliard equations with W1,1 kernel and singular potential. In: Differential Equations. Elsevier. 289, pp. 35-58. ISSN 0012-2661. eISSN 1608-3083. Available under: doi: 10.1016/j.jde.2021.04.016

@article{Davoli2021Local-55527, title={Local asymptotics for nonlocal convective Cahn-Hilliard equations with W1,1 kernel and singular potential}, year={2021}, doi={10.1016/j.jde.2021.04.016}, volume={289}, issn={0012-2661}, journal={Differential Equations}, pages={35--58}, author={Davoli, Elisa and Scarpa, Luca and Trussardi, Lara} }

We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in the case of a W<sup>1,1</sup> convolution kernel and under homogeneous Neumann conditions. Any type of potential, possibly also of double-obstacle or logarithmic type, is included. Additionally, we highlight variants and extensions to the setting of periodic boundary conditions and viscosity contributions, as well as connections with the general theory of evolutionary convergence of gradient flows. Trussardi, Lara terms-of-use eng Davoli, Elisa Scarpa, Luca 2021-11-12T12:08:13Z Scarpa, Luca Local asymptotics for nonlocal convective Cahn-Hilliard equations with W<sup>1,1</sup> kernel and singular potential Davoli, Elisa 2021-11-12T12:08:13Z 2021 Trussardi, Lara

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