The influence of nonlinear conduction on singularity formation in the intense plane-wave, nonlinear dielectric interaction problem

DOI10.1016/0898-1221(86)90175-6zbMath0614.35083OpenAlexW1975711226MaRDI QIDQ4722486

Frederick Bloom

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0898-1221(86)90175-6

zbMATH Keywords

singularitiesMaxwell's equationspropagationnonlinear Ohm's lawintense plane-wave pulsenonlinear dielectric half-space

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Analyticity in context of PDEs (35A20) Linear first-order PDEs (35F05) Electromagnetic theory (general) (78A25) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (5)

Global existence and asymptotic stability of solutions to the Cauchy problem for wave propagation in nonlinear dielectric media ⋮ A condition implying the global existence of \(C^ 1\) solutions for a class of nonlinear transmission lines ⋮ Formation of shock discontinuities for a class of nonlinear transmission lines ⋮ Almost global existence in the plane wave-nonlinear dielectric interaction problem ⋮ Long time existence of solutions for \({\partial{} ^ 2 \over{} \partial{} T^ 2} u(x,t) + {\partial{} \over{} \partial{} T} \alpha{} (u(x,t)) = {\partial{} ^ 2 \over{} \partial{} X^ 2} \beta{} (u(x,t))\)

Cites Work

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• Nonexistence of smooth electromagnetic fields in nonlinear dielectrics: Shock development in a half-space
• Instability of steady shearing flows in a non-linear viscoelastic fluid
• Formation and decay of electromagnetic shock waves
• Formation of singularities for wave equations including the nonlinear vibrating string
• Some Applications of the Riemann Method to Electromagnetic Wave Propagation in Nonlinear Media
• Breakdown of smooth solutions in dissipative nonlinear hyperbolic equations
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Some existence theorems for hyperbolic systems of partial differential equations in two independent variables
• Time reversal and spatial inversion in magnetoelectric and nonlinear optical phenomena

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