StableIF
Financiado
Stable interfaces phase transitions minimal surfaces and free boundaries
One of the main drivers of development for the theory of nonlinear elliptic PDE during the second half of the XX century has been the mathematical analysis of physical models for inter- faces. Depending on the specific model, thes...
One of the main drivers of development for the theory of nonlinear elliptic PDE during the second half of the XX century has been the mathematical analysis of physical models for inter- faces. Depending on the specific model, these interfaces are called minimal surfaces, phase transitions, free boundaries, etc. These models are very important in applications and, due to their strong geometric content and the interdisciplinary methods required for their study, also from a pure mathematics perspective. One of the simplest semilinear PDE exhibiting an interface is the classical Allen-Cahn equation. Originally proposed as a model for metal alloys, it gained mathematical notoriety due to its deep connection with the minimal surface equation and many other important PDE. It is very related to the Cahn-Hiliard equation (phase separation in binary fluids), to the Peierls-Nabarro equation (crystal dislocations), and to the Ginzburg-Landau theory (phase transitions, super-conductivity). In addition, it has similarities with other important models such as Bernoulli’s free boundary problem (flame propagation and shape optimization) or the Eriksen-Leslie system (liquid crystals). In the last four decades, outstanding works led to a very deep understanding of the structure of (absolute) energy minimizers for most of the previous models. Still, up to very few exceptions, almost nothing is known today on the structure of stable solutions —i.e. (roughly speaking) minimizers with respect to sufficiently small perturbations. Since stable solutions are the ones observable in Nature, their understanding is a fundamental question. Even though it is a very challenging mathematical problem, all the new analysis tools developed in the last decades plus some recent progress give us now an excellent opportunity to address it. In three words, the very ambitious goal of this ERC project is to understand stable interfaces.
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Duración del proyecto: 64 meses
Fecha Inicio: 2020-08-12
Fecha Fin: 2025-12-31
Fecha Fin: 2025-12-31
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2020-08-12
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2020-STG:
ERC STARTING GRANTS
Cerrada
hace 5 años
Presupuesto
El presupuesto total del proyecto asciende a
1M€
Líder del proyecto
EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
No se ha especificado una descripción o un objeto social para esta compañía.
341.26K€ |
Participante