The (2+1)D Parallel-plate System

This system was treated using MDWDFs in [62,211]. Now the dependent variables are a voltage , and current density components and ; these, and the sources , and are functions of time and two spatial variables, and . , , and are arbitrary smooth positive functions of and ( and are strictly positive). It is worth mentioning that the same equations can be used in the contexts of (2+1)D linear acoustics, the vibration of a membrane, and, with a trivial modification, (2+1)D electromagnetic field problems (involving TE or TM modes).

System (3.67) is symmetric hyperbolic, and thus has the form of (3.1), where , and with

It will follow, as in the case of the (1+1)D transmission line system (see §3.7.4), that the total energy of the MDKC that we will derive in the next section will be equal to the energy of system (3.67), as per (3.6).