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Introduction

  • Antonio André NovotnyEmail author
  • Jan Sokołowski
  • Antoni Żochowski
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 188)

Abstract

Mathematical analysis and numerical solutions of problems with unknown shapes or geometrical domains is a challenging and rich research field in the modern theory of the calculus of variations, partial differential equations, differential geometry as well as in numerical analysis. In this book, we describe some aspects of numerical solution for problems with unknown shapes, which use tools of asymptotic analysis with respect to small defects or imperfections to obtain sensitivity of shape functionals.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Antonio André Novotny
    • 1
    Email author
  • Jan Sokołowski
    • 2
    • 3
    • 4
  • Antoni Żochowski
    • 3
  1. 1.Coordenação de Métodos Matemáticos e ComputacionaisLaboratório Nacional de Computação Científica LNCC/MCTICPetrópolisBrazil
  2. 2.Institut Élie Cartan de Nancy, UMR 7502Université de Lorraine, CNRSVandœuvre-Lès-NancyFrance
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  4. 4.Universidade Federal da Paraiba, Centro de informaticaJoão PessoaBrazil

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