Lattice Dynamics Coupled at an Interface

Abstract

A coupled lattice dynamical system generated by two infinite lattice differential equations meeting asymptotically at an interface is studied. This can be interpreted as a special case of dynamics on graphs with the sum of inputs and outputs at each node satisfying the Kirchhoff balance law. First a suitable infinite sequence state space for the model is constructed. Then the existence and uniqueness of solutions and the generation of a dynamical system by the coupled equations is established. Finally, the existence of a global attractor of the coupled dynamical system is discussed. The analysis of the attractor is complicated by the fact that the attraction is in a weaker topology than that defining the state space of the coupled dynamics under which the state space is incomplete.