Global existence of classical solutions to the Cauchy problem for a kind of quasilinear hyperbolic system

DOI10.1016/J.NA.2008.12.044zbMath1173.35581OpenAlexW1984949654MaRDI QIDQ1030037

Yan Guan

Publication date: 1 July 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.12.044

zbMATH Keywords

Cauchy problemglobal existencequasilinear hyperbolic systemnull conditionslinear elastodynamic operator

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Shells (74K25) Second-order nonlinear hyperbolic equations (35L70) Higher-order hyperbolic systems (35L55) Initial value problems for second-order hyperbolic equations (35L15) Existence of solutions of dynamical problems in solid mechanics (74H20)

Cites Work

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• Nonresonance and global existence of prestressed nonlinear elastic waves
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• The global existence theorem for quasi-linear wave equations with multiple speeds
• An elementary proof of global or almost global existence for quasi-linear wave equations
• Global Existence for Systems of Nonlinear Wave Equations in 3D with Multiple Speeds
• Global behavior of solutions to nonlinear wave equations in three dimensions
• Global solutions of nonlinear hyperbolic equations for small initial data
• Blow-up for quasi-linear wave equations in three space dimensions

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