Existence and uniqueness of singular solutions for a conservation law arising in magnetohydrodynamics

DOI10.1088/1361-6544/aae04bzbMath1406.35188arXiv1803.01214OpenAlexW2793280498WikidataQ129020059 ScholiaQ129020059MaRDI QIDQ4644667

Henrik Kalisch, Darko Mitrović, Vincent Teyekpiti

Publication date: 8 January 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.01214

zbMATH Keywords

Riemann problemdelta shock wavesadmissibility conditionnonlinear change of variablesBrio systemmathematical entropy

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Magnetohydrodynamics and electrohydrodynamics (76W05)

Related Items (13)

Collision of solitons in non-integrable versions of the Degasperis-Procesi model ⋮ Formation of delta shock and vacuum state for the pressureless hydrodynamic model under the small disturbance of traffic pressure ⋮ Exact delta shock wave solution to the Riemann problem for the three-component chromatography model ⋮ On existence and admissibility of singular solutions for systems of conservation laws ⋮ Limiting behavior of scaled general Euler equations of compressible fluid flow ⋮ The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model ⋮ The vanishing pressure limits of Riemann solutions to the Isothermal two-phase flow model under the external force ⋮ Delta shock formation for the isothermal and logarithmic-corrected Chaplygin Euler equations ⋮ The Riemann problem for the one-dimensional isentropic Euler system under the body force with varying gamma law ⋮ Asymptotic limits of Riemann solutions to a novel second-order continuous macroscopic traffic flow model ⋮ Pressureless magnetohydrodynamics system: Riemann problem and vanishing magnetic field limit ⋮ Stability of delta shock solution for the simplified magnetohydrodynamics equations under the linear flux-function perturbation ⋮ Formation of vacuum state and delta shock wave for the relativistic Euler system for polytropic gas with the varying \(\gamma\)-law

Cites Work

• Unnamed Item
• Unnamed Item
• The Riemann problem for the Brio system: a solution containing a Dirac mass obtained via a distributional product
• One-dimensional nonlinear chromatography system and delta-shock waves
• The Riemann problem admitting \(\delta-, \delta ^{\prime }\)-shocks, and vacuum states (the vanishing viscosity approach)
• Shadow waves: Entropies and interactions for delta and singular shocks
• The entropy condition and the admissibility of shocks
• Dynamics of propagation and interaction of \(\delta\)-shock waves in conservation law systems
• Spaces of weighted measures for conservation laws with singular shock solutions
• Definition and weak stability of nonconservative products
• Vanishing viscosity solutions of nonlinear hyperbolic systems
• Delta shock waves in shallow water flow
• Higher order shadow waves and delta shock blow up in the Chaplygin gas
• Conserving the wrong variables in gas dynamics: A Riemann solution with singular shocks
• Hyperbolic conservation laws with large initial data. Is the Cauchy problem well-posed?
• Delta shock waves for the chromatography equations as self-similar viscosity limits
• Singular solutions of a fully nonlinear 2 × 2 system of conservation laws
• Hyperbolic systems of conservation laws II
• Measure solutions to a strictly hyperbolic system of conservation laws
• Existence and uniqueness of discontinuous solutions for a hyperbolic system
• A shallow-water system with vanishing buoyancy
• A kinematic conservation law in free surface flow
• Well posedness for pressureless flow

This page was built for publication: Existence and uniqueness of singular solutions for a conservation law arising in magnetohydrodynamics