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Free Boundary Problems in PDEs and Particle Systems

  • Gioia Carinci
  • Anna De Masi
  • Cristian Giardinà
  • Errico Presutti

Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 12)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
    Pages 1-3
  3. The Basic Model

    1. Front Matter
      Pages 5-5
    2. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 7-10
    3. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 11-20
    4. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 21-25
    5. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 27-29
    6. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 31-39
    7. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 41-45
    8. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 47-53
    9. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 55-59
    10. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 61-69
    11. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 71-84
  4. Variants of the Basic Model

    1. Front Matter
      Pages 85-85
    2. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 87-88
    3. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 89-95
    4. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 97-100
    5. Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 101-107
  5. Back Matter
    Pages 109-110

About this book

Introduction

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.

Keywords

transport phenomena heat transport mass transport heat equation mass transport inequalities hydrodynamic limit scaling limits Stefan problem Fick's law Dirichlet conditions flame propagation non-equilibrium statistical mechanics

Authors and affiliations

  • Gioia Carinci
    • 1
  • Anna De Masi
    • 2
  • Cristian Giardinà
    • 3
  • Errico Presutti
    • 4
  1. 1.Delft University of TechnologyDelftThe Netherlands
  2. 2.Dipartimento di MatematicaUniversita di L'AguilaL'AquilaItaly
  3. 3.Dipartimento di MatematicaUniversità di Modena e Reggio EmiliaModenaItaly
  4. 4.Gran Sasso Science InstituteL/AquilaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-33370-0
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-33369-4
  • Online ISBN 978-3-319-33370-0
  • Series Print ISSN 2197-1757
  • Series Online ISSN 2197-1765
  • Buy this book on publisher's site
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