Existence and asymptotic behavior of solutions to 2 ∗ 2 hyperbolic quadratic conservation laws with small viscosity

DOI10.1016/0362-546X(91)90220-UzbMath0768.35034OpenAlexW1978110458MaRDI QIDQ3980049

Huijiang Zhao, Yun-Guang Lu

Publication date: 26 June 1992

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(91)90220-u

zbMATH Keywords

energy estimatesCauchy problemunique global solutioninvariant regionsviscous solutions\(2\times 2\) parabolic initial value problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Hyperbolic conservation laws (35L65) Initial value problems for second-order parabolic equations (35K15)

Related Items (5)

Viscous solutions of quadratic conservation laws with umbilic points ⋮ Convergence of the viscosity method for some nonlinear hyperbolic systems ⋮ Existence and convergence of solutions to a singularly perturbed higher order partially differential equation ⋮ Solutions in the large for certain nonlinear parabolic systems in arbitrary spatial dimensions ⋮ Solutions in the large for certain nonlinear parabolic equations and applications

Cites Work

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• Existence and asymptotic behavior of solutions to inhomogeneous equations of elasticity with little viscosity
• The Riemann Problem Near a Hyperbolic Singularity: The Classification of Solutions of Quadratic Riemann Problems I
• The Riemann Problem Near a Hyperbolic Singularity II
• Nonlinear stability of shock waves for viscous conservation laws

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