  This paper is concerned with the Cauchy problem of a multivalued ordinary
differential equation governed by the hypergraph Laplacian, which describes the
diffusion of ``heat'' or ``particles'' on the vertices of hypergraph. We
consider the case where the heat on several vertices are manipulated internally
by the observer, namely, are fixed by some given functions. This situation can
be reduced to a nonlinear evolution equation associated with a time-dependent
subdifferential operator, whose solvability has been investigated in numerous
previous researches. In this paper, however, we give an alternative proof of
the solvability in order to avoid some complicated calculations arising from
the chain rule for the time-dependent subdifferential. As for results which
cannot be assured by the known abstract theory, we also discuss the continuous
dependence of solution on the given data and the time-global behavior of
solution.
