SUSTAINED SOLUTIONS FOR CONSERVATION LAWS

DOI10.1081/PDE-100002245zbMath0986.35064MaRDI QIDQ2747906

Robin L. Young

Publication date: 6 June 2002

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Lie algebrageometric nonlinearityexponentially growing modesGlimm-Lax theoremperiodic solutions to the full Euler equations

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Invariance and symmetry properties for PDEs on manifolds (58J70)

Cites Work

• Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions
• A nonlinear instability for \(3\times 3\) systems of conservation laws
• Global solution of the Cauchy problem for a class of 2x2 nonstrictly hyperbolic conservation laws
• The large time stability of sound waves
• Weak Stability in the Global L 1 -Norm for Systems of Hyperbolic Conservation Laws
• Resonantly Interacting Weakly Nonlinear Hyperbolic Waves. I. A Single Space Variable
• Some Explicit Resonating Waves in Weakly Nonlinear Gas Dynamics
• Formation of singularities in one-dimensional nonlinear wave propagation
• Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws
• Quasiperiodic Solutions in Weakly Nonlinear Gas Dynamics. Part I. Numerical Results in the Inviscid Case
• Some problems in the theory of quasilinear equations
• Solutions in the large for nonlinear hyperbolic systems of equations
• Systems of Conservation Equations with a Convex Extension
• The propagation of weak discontinuities in quasi-linear hyperbolic systems with discontinuous coefficients part I - fundamental theory^†

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