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

DOI10.1016/S0022-247X(02)00264-0zbMath1023.35077OpenAlexW2984745362MaRDI QIDQ1856844

Nguyen Thanh Long

Publication date: 11 February 2003

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

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00264-0

zbMATH Keywords

Galerkin methodasymptotic expansioncompactness argumentlinear recurrent sequenceKirchhoff-Carrier operator

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (14)

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. ⋮ Weighted Hardy operators and commutators on Morrey spaces ⋮ Stabilization for the Kirchhoff type equation from an axially moving heterogeneous string modeling with boundary feedback control ⋮ A mixed Dirichlet-Robin problem for a nonlinear Kirchhoff-carrier wave equation ⋮ 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 ⋮ CBMO estimates for multilinear Hardy operators ⋮ Asymptotic behavior of a nonlinear Kirchhoff type equation with spring boundary conditions ⋮ Unnamed Item ⋮ On a nonlinear Kirchhoff-Carrier wave equation associated with Robin conditions ⋮ On a nonlinear wave equation involving the term \(-\frac{\partial}{\partial x}(u(x,t,u,\|u_x\|^2)u_x)\): linear approximation and asymptotic expansion of solution in many small parameters ⋮ On the nonlinear wave equation \(u_{tt}-B(t,\| u \|^2, \| u_x\|^2)u_{xx}=f(x,t,u,u_x,u_t,\| u\|^2,\| u_x\|^2)\) associated with the mixed homogeneous conditions ⋮ High-order iterative schemes for a nonlinear Kirchhoff-Carrier wave equation associated with the mixed homogeneous conditions ⋮ A high order iterative scheme for a nonlinear Kirchhoff wave equation in the unit membrane ⋮ The \(n\)-order iterative schemes for a nonlinear Kirchhoff-Carrier wave equation associated with the mixed inhomogeneous conditions

Cites Work

• On some nonlinear perturbation of Kirchhoff-Carrier operator
• On the nonlinear vibrations equation with a coefficient containing an integral
• 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
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