Uniqueness of self-similar solutions to the Riemann problem for the Hopf equation with complex nonlinearity

DOI10.1134/S0965542516070113zbMath1362.35069MaRDI QIDQ519142

A. P. Chugainova, V. A. Shargatov, A. G. Kulikovskij

Publication date: 4 April 2017

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

shock wavesKdV-Burgers equationRiemann waves

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Self-similar solutions to PDEs (35C06)

Related Items (10)

Structures of non-classical discontinuities in solutions of hyperbolic systems of equations ⋮ Long nonlinear waves in anisotropic cylinders ⋮ Structures of longitudinal-torsional shock waves and special discontinuities in nonlinearly viscoelastic media with dispersion ⋮ Nonuniqueness of a self-similar solution to the Riemann problem for elastic waves in media with a negative nonlinearity parameter ⋮ Analytical description of the structure of special discontinuities described by a generalized KdV-Burgers equation ⋮ Stability of shock wave structures in nonlinear elastic media ⋮ Shock waves in anisotropic cylinders ⋮ Flow structure behind a shock wave in a channel with periodically arranged obstacles ⋮ Stability analysis of traveling wave solutions of a generalized Korteweg-de Vries-Burgers equation with variable dissipation parameter ⋮ Longitudinal and torsional shock waves in anisotropic elastic cylinders

Cites Work

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• Spectral stability of special discontinuities
• Stability of nonstationary solutions of the generalized KdV-Burgers equation
• Nonstationary solutions of a generalized Korteweg-de Vries-Burgers equation
• Stability of discontinuity structures described by a generalized KdV-Burgers equation
• Classical and non-classical discontinuities in solutions of equations of non-linear elasticity theory
• Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation

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