n this talk, we discuss local well-posedness for the Cauchy problem associated with the Korteweg-de Vries (KdV) equation on a general metric star graph. The graph comprises (m+k) semi-infinite edges: k negative half-lines and m positive half-lines, all joined at a common vertex. The choice of boundary conditions is compatible with the conditions determined by the semigroup theory. The crucial point in this work is to obtain the integral formula using the forcing operator method. This work extends the previous results obtained by [2018 Cavalcante] for the specific case of the $\mathcal Y$ junction to a more general class of star graphs.

It is a joint work with J. Marques Neto.