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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

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

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-IX
  2. Back Matter

    Pages 235-245

About this book

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
  • partial differential equations

Bibliographic Information

  • Book Title: Mathematical Aspects of Evolving Interfaces

  • Book Subtitle: 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

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b11357

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Softcover ISBN: 978-3-540-14033-7Published: 12 June 2003

  • eBook ISBN: 978-3-540-39189-0Published: 01 January 2003

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 248

  • Topics: Differential Equations, Differential Geometry, Classical and Continuum Physics, Thermodynamics

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 50.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions