Maximal quasi-accretive Laplacians on finite metric graphs


For a finite not necessarily compact metric graph, one considers the differential expression \({-\frac{d^2}{d x^2}}\) on each edge. The boundary conditions at the vertices of the graph yielding quasi-m-accretive as well as m-accretive operators are completely characterised.

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Correspondence to Amru Hussein.

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Hussein, A. Maximal quasi-accretive Laplacians on finite metric graphs. J. Evol. Equ. 14, 477–497 (2014).

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Mathematics Subject Classification (1991)

  • Primary 34B45
  • Secondary 35J05
  • 35K05
  • 47D06


  • Differential operators on metric graphs
  • Quasi-m-accretive Laplacians
  • Quasi-contractive semigroups