Abstract

I will discuss several situations when one has to perform limit passage from non-local to local operators in the context of the degenerate Cahn-Hilliard equation (i.e. with degenerate mobility). This includes kinetic derivation of the equation (Comm. Math. Phys., 2023; arXiv:2306.06486, with C. Elbar, M. Mason, B. Perthame), fairly classical problem of passage to the limit from non-local to local equation (JDE, 2023, with C. Elbar) and the same problem for aggregation-diffusion systems (arXiv:2303.11929, together with J. A. Carrillo, C. Elbar). Not all of these problems are fully understood and to some of them, complete solutions are available only on the torus.