Remarks on the point interaction approximation

  • R. Figari
  • G. Papanicolaou
  • J. Rubinstein
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 9)


The point interaction approximation is a way to study boundary value problems in regions with many small inclusions. For example, heat conduction in a material with many small holes that absorb heat, fluid flow in a region with many small obstacles, etc. The main idea is to replace the inclusions along with the boundary conditions on them by an inhomogeneous term in the differential equation which is then to hold evrywhere. As the name Point Interaction suggests, the effect of the inclusions is localized so the approximation is valid for small volume fractions. In this paper we shall consider the heat conduction problem as follows.


Continuum Limit Heat Conduction Problem Sphere Center Center Configuration Bubbly Liquid 
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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • R. Figari
    • 1
  • G. Papanicolaou
    • 2
  • J. Rubinstein
    • 3
  1. 1.Department of Theoretical PhysicsUniversity of NaplesNaplesItaly
  2. 2.Courant InstituteNew York UniversityNew YorkUSA
  3. 3.Department of MathematicsStanford UniversityStanfordUSA

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