Formation of shock discontinuities for a class of nonlinear transmission lines

DOI10.1016/0898-1221(88)90273-8zbMath0671.35057OpenAlexW2056751655MaRDI QIDQ1119831

Frederick Bloom

Publication date: 1988

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(88)90273-8

zbMATH Keywords

nonexistenceshocksRiemann invariantsinitial datacharacteristic curvesdistributed parameter nonlinear transmission linequasilinear hyperbolic system of equations

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) First-order nonlinear hyperbolic equations (35L60) Electromagnetic theory (general) (78A25)

Related Items (2)

Existence and asymptotic behavior of smooth solutions for the nonlinear transmission line problem ⋮ Global existence of weak solutions to the nonlinear transmission line problem

Cites Work

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• A condition implying the global existence of \(C^ 1\) solutions for a class of nonlinear transmission lines
• Instability of steady shearing flows in a non-linear viscoelastic fluid
• A model for one-dimensional, nonlinear viscoelasticity
• The influence of nonlinear conduction on singularity formation in the intense plane-wave, nonlinear dielectric interaction problem
• Breakdown of smooth solutions in dissipative nonlinear hyperbolic equations
• Nonlinear Effects in Transmission Lines

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