• Application of Newton’s method to a homogenization problem

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/090/03/0229-0238

    • Keywords

       

      Elliptic; homogenization; Newton’s method; semilinear

    • Abstract

       

      The homogenization of a family (Pε) of uniformly elliptic semilinear partial differential equations of second order is studied. The main result is that any non-singular solutionu of the homogenized problem (P) is the limit of non-singular solutions of (Pε). The method consists of specifying a functionwε starting from which the Newton iterates converge to a solutionuε ofPε. These solutionsuε converge to the given solutionu of (P).

    • Author Affiliations

       

      S Kesavan1

      1. TIFR Centre, Indian Institute of Science Campus, Bangalore - 560 012, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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