Partial Differential Equations on Graphs

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


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].


Partial Differential Equation Elliptic Problem Domain Decomposition Multiple Node Transmission Condition 
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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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