Global regularity and formation of singularities of solutions to first order quasilinear hyperbolic systems

DOI10.1017/S0308210500015195zbMath0453.35056OpenAlexW2327391924MaRDI QIDQ3900411

Ta-Tsien Li

Publication date: 1981

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/s0308210500015195

zbMATH Keywords

Cauchy problemeigenvaluesglobal regularityinitial dataformation of singularitiesfirst order quasilinear hyperbolic systems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) First-order nonlinear hyperbolic equations (35L60)

Related Items (10)

The global Hölder-continuous solution of isentropic gas dynamics ⋮ Existence of globally bounded continuous solutions for nonisentropic gas dynamics equations ⋮ Global structure instability of Riemann solutions for general quasilinear hyperbolic systems of conservation laws in the presence of a boundary ⋮ Cauchy problem for weakly linearly degenerate hyperbolic systems in diagonal form. ⋮ Exact solutions to a class of quasilinear hyperbolic systems ⋮ Blow up of periodic solutions to quasilinear hyperbolic systems ⋮ Global smooth solution of the nonisentropic gas dynamics system ⋮ Blow-up of solutions to the initial-boundary value problem for quasilinear hyperbolic systems of conservation laws ⋮ Formation of singularities for certain hyperbolic systems in one space dimension. ⋮ On the breakdown of solutions to \(N\times N\) quasilinear hyperbolic systems

Cites Work

• Unnamed Item
• The occurrence of singularities in solutions of homogeneous systems of two first order quasilinear hyperbolic equations with smooth initial data
• Periodic vibrations of systems governed by nonlinear partial differential equations
• 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

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