Existence and asymptotic behavior of smooth solutions for the nonlinear transmission line problem

Abstract

For a distributed parameter nonlinear transmission line with constant self-inductance and resistance, but voltage-dependent capacitance and leakage conductance, we establish for small data the existence of global C² solutions to the (nonlinearly) damped nonlinear wave equation which governs the evolution of the charge in the line; the energy method employed to establish the global existence theorem also yields new results on the asymptotic behavior of the charge distribution in the line as t —► +00

Keywords:

• Transmission line
• asymptotic behaviour
• damped nonlinear wave equation

AMS(MOS):

• 35L78

_#The research of the second author was supported, in part, by NSF Grant DMS 8823037

_#The research of the second author was supported, in part, by NSF Grant DMS 8823037

Notes

_#The research of the second author was supported, in part, by NSF Grant DMS 8823037