On the nonlinear wave equation \(u_{tt}-B(t,\|u\|^2, \|u_{x}\|^2, \|u_t\|^2)u_{xx}= f(x,t,u,u_x,u_t,\|u\|^2,\|u_x\|^2,\|u_t\|^2)\) associated with mixed homogeneous conditions.

DOI10.1016/j.na.2004.05.021zbMath1053.35107OpenAlexW1557871660MaRDI QIDQ1883106

Nguyen Thanh Long

Publication date: 1 October 2004

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.2004.05.021

zbMATH Keywords

Kirchhoff equationone space dimensionlinear recursive schemesemilinear right-hand side

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Asymptotic expansions of solutions to PDEs (35C20)

Cites Work

• On some nonlinear perturbation of Kirchhoff-Carrier operator
• On the nonlinear wave equation \(u_{tt}-B(\|u_{x} {\|}^{2})u_{xx}\) = \(f(x,t,u,u_{x},u_{t},{\|}u_{x}{\|}^{2})\) associated with the mixed homogeneous conditions
• On the nonlinear vibrations equation with a coefficient containing an integral
• On the nonlinear wave equation \(u_{tt}-B(t,\|u_{x}\|^{2})u_{xx} = f(x,t,u,u_{x},u_{t})\) associated with the mixed homogeneous conditions
• Local solutions for a nonlinear degenerate Hyperbolic equation
• Linear Recursive Schemes Associated with Some Nonlinear Partial Differential Equations in One Dimension and the Tau Method
• ON A CLASS OF QUASILINEAR HYPERBOLIC EQUATIONS
• On the nonlinear wave equation uu - uxx = f(x,t,u,ux,ut) associated with the mixed homogenous conditions
• On the non-linear vibration problem of the elastic string
• Asymptotic expansion of the solution for nonlinear wave equation with the mixed homogeneous conditions
• Linear recursive schemes and asymptotic expansion associated with the Kirchhoff-Carrier operator
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