JournalsprimsVol. 43, No. 4pp. 945–961

Poisson Equations with Nonlinear Source Terms on Networks

  • Soon-Yeong Chung

    Sogang University, Seoul, South Korea
  • Dohan Kim

    Seoul National University, South Korea
  • Nam Kee Lee

    Seoul National University, South Korea
Poisson Equations with Nonlinear Source Terms on Networks cover

Abstract

C. Berenstein and the first author introduced an elliptic operator ∆_ω_ and an ω-harmonic function on graphs, with its physical interpretation as a diffusion equation on graphs, which models electric networks. They also proved the solvability of the problems such as the Dirichlet and Neumann boundary value problems for the Laplace equation and the Poisson equation on networks. In this paper, we consider the Poisson equation with nonlinear source term on networks and show the existence and the uniqueness of a solution with suitable source term.

Cite this article

Soon-Yeong Chung, Dohan Kim, Nam Kee Lee, Poisson Equations with Nonlinear Source Terms on Networks. Publ. Res. Inst. Math. Sci. 43 (2007), no. 4, pp. 945–961

DOI 10.2977/PRIMS/1201012375