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Free Boundary Problems in PDEs and Particle Systems

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

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-vii
  2. Introduction

    • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
    Pages 1-3
  3. The Basic Model

    1. Front Matter

      Pages 5-5
    2. Introduction to Part I

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 7-10
    3. The Basic Model, Definitions and Results

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 11-20
    4. Regularity Properties of the Barriers

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 21-25
    5. Lipschitz and \(L^1\) Estimates

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 27-29
    6. Mass Transport Inequalities

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 31-39
    7. The Limit Theorems on Barriers

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 41-45
    8. Brownian Motion and the Heat Equation

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 47-53
    9. Existence of Optimal Sequences

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 55-59
    10. Proof of the Main Theorem

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 61-69
    11. The Basic Particle Model and Its Hydrodynamic Limit

      • 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. Introduction to Part II

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 87-88
    3. Independent Walkers with Current Reservoirs

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 89-95
    4. Beyond Diffusive Scaling

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 97-100
    5. Other Models

      • Gioia Carinci, Anna De Masi, Cristian Giardinà, Errico Presutti
      Pages 101-107
  5. Back Matter

    Pages 109-110

About this book

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.

Authors and Affiliations

  • Delft University of Technology, Delft, The Netherlands

    Gioia Carinci

  • Dipartimento di Matematica, Universita di L'Aguila, L'Aquila, Italy

    Anna De Masi

  • Dipartimento di Matematica, Università di Modena e Reggio Emilia, Modena, Italy

    Cristian Giardinà

  • Gran Sasso Science Institute, L/Aquila, Italy

    Errico Presutti

Bibliographic Information

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access