Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms

DOI10.1017/S0308210500027074zbMath0899.35059OpenAlexW2110621559MaRDI QIDQ4374796

Huijiang Zhao, Changjiang Zhu, Tong Yang

Publication date: 10 November 1998

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500027074

zbMATH Keywords

small initial datagas dynamicsfluid dynamicselasto-dynamicsgeneralized Lax transformation

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Initial value problems for first-order hyperbolic systems (35L45)

Related Items (11)

The global classical solution to compressible Euler system with velocity alignment ⋮ Global solutions with shock waves to the generalized Riemann problem for a system of hyperbolic conservation laws with linear damping ⋮ Existence of a classical solution to complex material flow problems ⋮ Global classical solutions near vacuum to the initial-boundary value problem of isentropic flows through divergent ducts ⋮ Global existence of classical solutions for the gas flows near vacuum through ducts expanding with space and time ⋮ Smooth solution of multi-dimensional nonhomogeneous conservation law: its formula, and necessary and sufficient blowup criterion ⋮ Convergence to strong nonlinear diffusion waves for solutions of \(p\)-system with damping ⋮ Existence of global smooth solution to the initial boundary value problem for \(p\)-system with damping ⋮ GLOBAL WEAKLY DISCONTINUOUS SOLUTIONS TO THE MIXED INITIAL–BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS ⋮ The mixed initial-boundary value problem for quasilinear hyperbolic systems with linearly degenerate characteristics ⋮ Asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping. II

Cites Work

• Remarks on the maximum principle for parabolic equations and its applications
• Globally smooth solutions of quasilinear hyperbolic systems in diagonal form
• Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations
• Convergence of The Lax–Friedrichs' Scheme For Equaitons of Isentropic Gas Dynamics in Lagrangian Coordinates^∗
• Formation of singularities in one-dimensional nonlinear wave propagation
• Global resolvability for a viscoelastic model with relaxation
• Solutions in the large for certain nonlinear parabolic equations and applications
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Global continuous solutions of hyperbolic systems of quasi-linear equations
• Some existence theorems for hyperbolic systems of partial differential equations in two independent variables
• Unnamed Item

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