The Cauchy problem for general nonlinear wave equations with doubly dispersive

DOI10.3934/cam.2024019zbMATH Open1548.35086MaRDI QIDQ6612035

Runzhang Xu, Yue Pang, Xiaotong Qiu, Yanbing Yang

Publication date: 27 September 2024

Published in: Communications in Analysis and Mechanics (Search for Journal in Brave)

zbMATH Keywords

wave equationCauchy problemblow-upqualitative behaviordoubly dispersive

Mathematics Subject Classification ID

Weak solutions to PDEs (35D30) Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Second-order semilinear hyperbolic equations (35L71)

Cites Work

• Unnamed Item
• Instability of solitary waves for generalized Boussinesq equations
• Global existence and blow-up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations
• Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation
• Decay and scattering of solutions for a generalized Boussinesq equation
• Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation
• Nonlinear elastic waves in rods
• Global well-posedness for a class of fourth-order nonlinear strongly damped wave equations
• Global well-posedness of coupled parabolic systems
• Potential well method for Cauchy problem of generalized double dispersion equations
• Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations
• Initial boundary value problem for semilinear hyperbolic equations and parabolic equations with critical initial data
• Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity

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