Application of Lagrangian with reverse time scales to transients in RC-transmission lines. I. Propagation

Lagrangian for diffusion equation is formulated in context of a newly developed variational theory for dissipative systems with distributed parameters. This Lagrangian is used to determine approximate solutions for diffusion along a semi-infinite RC transmission line, energized by a constant current source. Two solutions are obtained by radically different test functions: one, which simulates propagation and another, which represents instantaneous diffusion. Both solutions approximate the exact solution very well, thus confirming the new Lagrangian