caa a22 4500 605496358 CHVBK 20210128100536.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10231-014-0411-9 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0411-9 Cahn-Hilliard equation with nonlocal singular free energies [Elektronische Daten] [Helmut Abels, Stefano Bosia, Maurizio Grasselli] We consider a Cahn-Hilliard equation which is the conserved gradient flow of a nonlocal total free energy functional. This functional is characterized by a Helmholtz free energy density, which can be of logarithmic type. Moreover, the spatial interactions between the different phases are modeled by a singular kernel. As a consequence, the chemical potential $$\mu $$ μ contains an integral operator acting on the concentration difference $$c$$ c , instead of the usual Laplace operator. We analyze the equation on a bounded domain subject to no-flux boundary condition for $$\mu $$ μ and by assuming constant mobility. We first establish the existence and uniqueness of a weak solution and some regularity properties. These results allow us to define a dissipative dynamical system on a suitable phase-space, and we prove that such a system has a (connected) global attractor. Finally, we show that a Neumann-like boundary condition can be recovered for $$c$$ c , provided that it is supposed to be regular enough. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Cahn-Hilliard equation nationallicence Nonlocal free energy nationallicence Regional fractional Laplacian nationallicence Logarithmic potential nationallicence Monotone operators nationallicence Global attractors nationallicence Abels Helmut Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany aut Bosia Stefano Politecnico di Milano, Dipartimento di Matematica, 20133, Milan, Italy aut Grasselli Maurizio Politecnico di Milano, Dipartimento di Matematica, 20133, Milan, Italy aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 1071-1106 0373-3114 194:4<1071 2015 194 10231 https://doi.org/10.1007/s10231-014-0411-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0411-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Abels Helmut Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany aut NATIONALLICENCE 700 1- Bosia Stefano Politecnico di Milano, Dipartimento di Matematica, 20133, Milan, Italy aut NATIONALLICENCE 700 1- Grasselli Maurizio Politecnico di Milano, Dipartimento di Matematica, 20133, Milan, Italy aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 1071-1106 0373-3114 194:4<1071 2015 194 10231