In this talk, we consider finite horizon optimal control problems on multi-domains which are composed by a group of disjoint subdomains. The proper definition of solution to the corresponding Hamilton-Jacobi-Bellman equation becomes a delicate issue due to the discontinuity of the Hamiltonian on the interfaces between the subdomains. We will discuss the junction conditions on the interfaces which allow to deduce the existence, uniqueness and stability results of the solution. This is based on the joint work with Daria Ghilli and Hasnaa Zidani.