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.
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Gioia Carinci Anna De Masi Cristian Giardinà Errico Presutti
Free Boundary Problems in PDEs and Particle Systems 123
SpringerBriefs in Mathematical Physics Volume 12
Series editors Nathanaël Berestycki, Cambridge, UK Mihalis Dafermos, Cambridge, UK Tohru Eguchi, Tokyo, Japan Atsuo Kuniba, Tokyo, Japan Matilde Marcolli, Pasadena, USA Bruno Nachtergaele, Davis, USA
More information about this series at http://www.springer.com/series/11953
Gioia Carinci Anna De Masi Cristian Giardinà Errico Presutti •
•
Free Boundary Problems in PDEs and Particle Systems
123
Gioia Carinci Delft University of Technology Delft The Netherlands Anna De Masi Dipartimento di Matematica Universita di L’Aguila L’Aquila Italy
Cristian Giardinà Dipartimento di Matematica Università di Modena e Reggio Emilia Modena Italy Errico Presutti Gran Sasso Science Institute L’Aquila Italy
ISSN 2197-1757 ISSN 2197-1765 (electronic) SpringerBriefs in Mathematical Physics ISBN 978-3-319-33369-4 ISBN 978-3-319-33370-0 (eBook) DOI 10.1007/978-3-319-33370-0 Library of Congress Control Number: 2016940811 © The Author(s) 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Part I
1
The Basic Model
2
Introduction to Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 10
3
The Basic Model, Definitions and Results . . . . 3.1 The Basic Problem. . . . . . . . . . . . . . . . . 3.2 Stationary Solutions . . . . . . . . . . . . . . . . 3.3 The FBP for the Basic Model . . . . . . . . . 3.4 Main Theorem: Existence and Uniqueness 3.5 The Upper and Lower Barriers . . . . . . . . 3.6 Mass Transport . . . . . . . . . . . . . . . . . . .
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