Cahn-Hilliard equation with nonlocal singular free energies
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| 003 | CHVBK | ||
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| 008 | 210128e20150801xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10231-014-0411-9 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0411-9 | ||
| 245 | 0 | 0 | |a Cahn-Hilliard equation with nonlocal singular free energies |h [Elektronische Daten] |c [Helmut Abels, Stefano Bosia, Maurizio Grasselli] |
| 520 | 3 | |a 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. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Cahn-Hilliard equation |2 nationallicence | |
| 690 | 7 | |a Nonlocal free energy |2 nationallicence | |
| 690 | 7 | |a Regional fractional Laplacian |2 nationallicence | |
| 690 | 7 | |a Logarithmic potential |2 nationallicence | |
| 690 | 7 | |a Monotone operators |2 nationallicence | |
| 690 | 7 | |a Global attractors |2 nationallicence | |
| 700 | 1 | |a Abels |D Helmut |u Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany |4 aut | |
| 700 | 1 | |a Bosia |D Stefano |u Politecnico di Milano, Dipartimento di Matematica, 20133, Milan, Italy |4 aut | |
| 700 | 1 | |a Grasselli |D Maurizio |u Politecnico di Milano, Dipartimento di Matematica, 20133, Milan, Italy |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 1071-1106 |x 0373-3114 |q 194:4<1071 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0411-9 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0411-9 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Abels |D Helmut |u Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bosia |D Stefano |u Politecnico di Milano, Dipartimento di Matematica, 20133, Milan, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Grasselli |D Maurizio |u Politecnico di Milano, Dipartimento di Matematica, 20133, Milan, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 1071-1106 |x 0373-3114 |q 194:4<1071 |1 2015 |2 194 |o 10231 | ||