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Free boundary problems in PDEs and particle systems

In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interacti...

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Detalles Bibliográficos
Autores principales: Carinci, Gioia, De Masi, Anna, Giardinà, Cristian, Presutti, Errico
Lenguaje:eng
Publicado: Springer 2016
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-33370-0
http://cds.cern.ch/record/2196696
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author Carinci, Gioia
De Masi, Anna
Giardinà, Cristian
Presutti, Errico
author_facet Carinci, Gioia
De Masi, Anna
Giardinà, Cristian
Presutti, Errico
author_sort Carinci, Gioia
collection CERN
description In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases. All the models discussed in this volume have an interest in problems arising in several research fields such as heat conduction, queuing theory, propagation of fire, interface dynamics, population dynamics, evolution of biological systems with selection mechanisms. In general researchers interested in the relations between PDE’s and stochastic processes can find in this volume an extension of this correspondence to modern mathematical physics.
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spelling cern-21966962021-04-21T19:38:48Zdoi:10.1007/978-3-319-33370-0http://cds.cern.ch/record/2196696engCarinci, GioiaDe Masi, AnnaGiardinà, CristianPresutti, ErricoFree boundary problems in PDEs and particle systemsMathematical Physics and MathematicsIn this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases. All the models discussed in this volume have an interest in problems arising in several research fields such as heat conduction, queuing theory, propagation of fire, interface dynamics, population dynamics, evolution of biological systems with selection mechanisms. In general researchers interested in the relations between PDE’s and stochastic processes can find in this volume an extension of this correspondence to modern mathematical physics.Springeroai:cds.cern.ch:21966962016
spellingShingle Mathematical Physics and Mathematics
Carinci, Gioia
De Masi, Anna
Giardinà, Cristian
Presutti, Errico
Free boundary problems in PDEs and particle systems
title Free boundary problems in PDEs and particle systems
title_full Free boundary problems in PDEs and particle systems
title_fullStr Free boundary problems in PDEs and particle systems
title_full_unstemmed Free boundary problems in PDEs and particle systems
title_short Free boundary problems in PDEs and particle systems
title_sort free boundary problems in pdes and particle systems
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-33370-0
http://cds.cern.ch/record/2196696
work_keys_str_mv AT carincigioia freeboundaryproblemsinpdesandparticlesystems
AT demasianna freeboundaryproblemsinpdesandparticlesystems
AT giardinacristian freeboundaryproblemsinpdesandparticlesystems
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