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Partial Differential Equations on Graphs

  • John E. Lagnese
  • Günter Leugering
Chapter
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 148)

Abstract

In this chapter we focus on one-dimensional partial differential equations on graphs. Partial differential equations on graphs, or on higher-dimensional ‘networked’ domains, have frequently been considered in the literature, beginning with the work of G. Lumber. We dispense with displaying a list of papers on this topic, but rather refer the reader to a recent proceedings volume [2] for an account of current research in this area. For higher-dimensional problems and, more importantly, for optimal control problems for partial differential equations on graphs or networked domains, see [61].

Keywords

Partial Differential Equation Elliptic Problem Domain Decomposition Multiple Node Transmission Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • John E. Lagnese
    • 1
  • Günter Leugering
    • 2
  1. 1.Department of MathematicsGeorgetown UniversityUSA
  2. 2.Angewandte Mathematik IIUniversität Erlangen NürnbergErlangenGermany

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