The Riemann problem of the Burgers equation with a discontinuous source term

DOI10.1016/j.jmaa.2012.05.021zbMath1246.35156OpenAlexW2058178397MaRDI QIDQ441983

Beixiang Fang, Pingfan Tang, Ya-Guang Wang

Publication date: 8 August 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.05.021

zbMATH Keywords

Burgers equationRiemann problemsentropy solutionsweak discontinuities``vacuum regionsappearance and disappearance of new shockscurved shocks and rarefaction wavesdiscontinuous source terms

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Shock waves and blast waves in fluid mechanics (76L05) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (6)

Shock waves for the hyperbolic balance laws with discontinuous sources ⋮ Eulerian droplet model: delta-shock waves and solution of the Riemann problem ⋮ Singular solutions to the Riemann problem for the pressureless Euler equations with discontinuous source term ⋮ A <scp>least‐squares</scp> finite element method based on the Helmholtz decomposition for hyperbolic balance laws ⋮ A new finite volume approach for transport models and related applications with balancing source terms ⋮ The shock wave solution to the Riemann problem for the Burgers equation with the linear forcing term

Cites Work

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• Hyperbolic conservation laws with relaxation
• The generic solution of the Riemann problem in a neighborhood of a point of resonance for systems of nonlinear balance laws
• Local existence and finite-time blow-up in multidimensional radiation hydrodynamics
• The Riemann Problem for an Inhomogeneous Conservation Law Without Convexity
• Formation of singularities of solutions to the three-dimensional Euler–Boltzmann equations in radiation hydrodynamics
• Nonlinear resonance for quasilinear hyperbolic equation
• A Bound on the Total Variation of the Conserved Quantities for Solutions of a General Resonant Nonlinear Balance Law
• Convergence of the $2 \times 2$ Godunov Method for a General Resonant Nonlinear Balance Law
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES

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