Advertisement

Mathematical Aspects of Evolving Interfaces

Lectures given at the C.I.M.-C.I.M.E. joint Euro-Summer School held in Madeira, Funchal, Portugal, July 3-9, 2000

  • Authors
  • Luigi Ambrosio
  • Klaus Deckelnick
  • Gerhard Dziuk
  • Masayasu Mimura
  • Vsevolod A. Solonnikov
  • Halil Mete Soner

Part of the Lecture Notes in Mathematics book series (LNM, volume 1812)

Table of contents

About this book

Introduction

Interfaces are geometrical objects modelling free or moving boundaries and arise in a wide range of phase change problems in physical and biological sciences, particularly in material technology and in dynamics of patterns. Especially in the end of last century, the study of evolving interfaces in a number of applied fields becomes increasingly important, so that the possibility of describing their dynamics through suitable mathematical models became one of the most challenging and interdisciplinary problems in applied mathematics. The 2000 Madeira school reported on mathematical advances in some theoretical, modelling and numerical issues concerned with dynamics of interfaces and free boundaries. Specifically, the five courses dealt with an assessment of recent results on the optimal transportation problem, the numerical approximation of moving fronts evolving by mean curvature, the dynamics of patterns and interfaces in some reaction-diffusion systems with chemical-biological applications, evolutionary free boundary problems of parabolic type or for Navier-Stokes equations, and a variational approach to evolution problems for the Ginzburg-Landau functional.

Keywords

Mean curvature Navier-Stokes equation curvature differential equation dynamics for Ginzburg-Landau functional dynamics of patterns and interfaces free boundary problems mean curvature flow optimal transport

Bibliographic information

  • DOI https://doi.org/10.1007/b11357
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-14033-7
  • Online ISBN 978-3-540-39189-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site