Globally smooth solutions of quasilinear hyperbolic systems in diagonal form

DOI10.1016/0022-247X(82)90266-9zbMath0488.35057MaRDI QIDQ1166023

David Hoff

Publication date: 1982

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

zbMATH Keywords

Cauchy problemmonotonicity conditionspreservation of smoothness

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) First-order nonlinear hyperbolic equations (35L60) PDEs with low regular coefficients and/or low regular data (35R05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (10)

Existence of second order smooth solutions for 2D Euler equations with symmetry outside a core region ⋮ Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms ⋮ Global resolvability for a viscoelastic model with relaxation ⋮ Global smooth solution of the nonisentropic gas dynamics system ⋮ On the global continuous solvability of the mixed problem for one-dimensional hyperbolic systems of quasilinear equations ⋮ Existence of global smooth solution to the relativistic Euler equations ⋮ Global smooth solution for nonlinearly damped_p-system with large initial data ⋮ Formation of singularities for certain hyperbolic systems in one space dimension. ⋮ On the breakdown of solutions to \(N\times N\) quasilinear hyperbolic systems ⋮ Hyperbolic Whitham systems and integrable equations

Cites Work

• A constructive theory for shock-free, isentropic flow
• Locally Lipschitz solutions of a single conservation law in several space variables
• Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations
• Formation of singularities in one-dimensional nonlinear wave propagation
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Nonlinear Hyperbolic Differential Equations for Functions of Two Independent Variables
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