Nonlocal phase transitions in homogeneous and periodic media
We discuss some results related to a phase transition model in which the potential energy induced by a double-well function is balanced by a fractional elastic energy. In particular, we present asymptotic results (such as GG -convergence, energy bounds and density estimates for level sets), flatness...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/104173 |
| Acceso en línea: | https://hdl.handle.net/2117/104173 https://dx.doi.org/10.1007/s11784-016-0359-z |
| Access Level: | acceso abierto |
| Palabra clave: | Chaotic behavior in systems Nonlocal Ginzburg-Landau-Allen-Cahn equation De Giorgi conjecture Planelike minimizers Chaotic orbits Càlcul de variacions Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Càlcul de variacions |
| Sumario: | We discuss some results related to a phase transition model in which the potential energy induced by a double-well function is balanced by a fractional elastic energy. In particular, we present asymptotic results (such as GG -convergence, energy bounds and density estimates for level sets), flatness and rigidity results, and the construction of planelike minimizers in periodic media. Finally, we consider a nonlocal equation with a multiwell potential, motivated by models arising in crystal dislocations, and we construct orbits exhibiting symbolic dynamics, inspired by some classical results by Paul Rabinowitz. |
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