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Publication Cover
Applicable Analysis
An International Journal
Volume 39, 1990 - Issue 1
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Original Articles

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

Hamid Bellout Dept. of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115
&
Frederick Bloom Dept. of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115
Pages 35-57 | Received 10 Apr 1990, Published online: 02 May 2007

References

  • Jeffrey , A. 1966 . Wave Propagation and ELectromagnetic Shock Wave Formation in Transmission Lines . J. Math. Mech , 15 : 1 – 13 .
  • Landauer , R. 1960 . Shock Waves in Nonlinear Transmission Lines and Their Effect on Parametric Amplification . IBM J , 1 : 391 – 401 .
  • Oumberbatch , E. 1967 . Nonlinear Effects in Transmission Lines . SIAM J, Appl. Math , 15 : 450 – 463 .
  • Kataev , I. G. 1966 . Electromagnetic Shock Waves , London : Iliffe Pub .
  • Bloom , F. 1988 . Formation of Shock Discontinuities for a Class of Nonlinear Transmission Lines . Comput. Math, Applic , 15 : 459 – 472 .
  • Nishida , J. 1976 . Global Smooth Solutions for the Second-Order Quasilinear Wave Equation with First-Order Dissipation . Univ, of Wisconsin , 15
  • Slemrod , M. 1978 . Instability of Steady Shearing Flows in a Nonlinear Viscoelastic Fluid . Arch, Rat Mech. Anal , 68 : 211 – 225 .
  • Bloom , F. 1987 . A Condition Implying the Global Existence of Cl Solutions for a Claas of Nonlinear Transmisison Lines . Comput. Math. Applic , 13 : 861 – 879 .
  • Wang , J. Wave Propagation Problem in a Nonlinear Transmission Lines , SIAM J. Anal .
  • Bloom , F. 1986 . Influence of Nonlinear Conduction on Shock Formation in the Intense Plane Wave-Nonlinear Dielectric Interaction Problem . Advances in Hyperbolic Partial Differential Equations , 3 : 477 – 489 .
  • Bellout , H. and Bloom , F. Global Existence and Asymptotic Stability of Solutions to the Cauchy Problem for Wave Propagation in Nonlinear Dielectric Media
  • Matsumura , A. 1977 . Global Existence and Asymptotics of the Solutions of the Second Order Quasilinear Hyperbolic Equations with First Order Dissipation . Inst. Math. Sci , 18 : 349 – 379 .
  • Dafermos , C, M. and Nohel , J. A. 1979 . Energy Methods for Nonlinear Hyperbolic Volterra Intergrodifferential Equations . Comm. in Partial Differential Equations , 18 : 219 – 278 .
  • Dafermos , C. M. and Nohel , J. A. 1981 . A Nonlinear Hyperbolic Volterra Equation in Viscoelasticity . Am. J.Math , 18 : 87 – 16 .
  • Hrusa , W. J. and Nohel , J. A. 1984 . Global Existence and Asymptotics in One-Dimensional Nonlinear Viscoelasticity . Appl. Pure MechLecture Notes in Physics , 195 : 165 – 187 .
  • Slemrod , M. 1981 . Global Existence, Uniqueness, and Asymptotic Stability of Classical Smooth Solutions in One-Dimensional . Arch, Rat. Mech. Anal , 76 : 97 – 133 .
  • Hrusa , W. J. 1983 . A Nonlinear Functional Differential Equation in Banach Space with Applications to Materials with Fading Memory . Arch. Rat. Mech. Anal , 84 : 99 – 137 .
  • Coleman , B. D. and Hrusa , W. J. 1986 . Stability of Equilibrium for a Nonlinear Hyperbolic System Describing Heat Propagation by Second Sound in Solids . Arch. Rat. Mech. Anal , 84 : 267 – 289 .
  • Bellout , H.F. and Bloom . 1986 . Global Existence of Weak Solutions to the Cauchy Problem for a Non-Linear Transmission Line . Nonlinear Analysis , 84

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