A condition implying the global existence of C1 solutions for a class of nonlinear transmission lines

Abstract

For a distributed parameter nonlinear transmission line, with constant self-inductance and resistance, but voltage-dependent capacitance and leakage conductance, a condition on the growth, in time, of the leakage conductance is proposed which implies the existence of global C 1 solutions to the inhomogeneous, damped, quasilinear hyperbolic system, with periodic initial data, which governs the evolution of the charge and current in the line. For a transmission line in which the leakage conductance may be controllable, in time, the analysis suggests a direct means of preventing the formation of shocks in the line.