JournalsprimsVol. 43, No. 3pp. 699–726

Diffusion and Elastic Equations on Networks

  • Soon-Yeong Chung

    Sogang University, Seoul, South Korea
  • Yun-Sung Chung

    Sungkyunkwan University, Suwon, South Korea
  • Jong-Ho Kim

    National Institute for Mathematical Sciences, Daejeon, South Korea
Diffusion and Elastic Equations on Networks cover
Download PDF

Abstract

In this paper, we discuss discrete versions of the heat equations and the wave equations, which are called the ω-diffusion equations and the ω-elastic equations on graphs. After deriving some basic properties, we solve the ω-diffusion equations under (i) the condition that there is no boundary, (ii) the initial condition and (iii) the Dirichlet boundary condition. We also give some additional interesting properties on the ω-diffusion equations, such as the minimum and maximum principles, Huygens property and uniqueness via energy methods. Analogues of the ω-elastic equations on graphs are also discussed.

Cite this article

Soon-Yeong Chung, Yun-Sung Chung, Jong-Ho Kim, Diffusion and Elastic Equations on Networks. Publ. Res. Inst. Math. Sci. 43 (2007), no. 3, pp. 699–726

DOI 10.2977/PRIMS/1201012039