On a nonlinear wave equation of Kirchhoff-carrier type: linear approximation and asymptotic expansion of solution in a small parameter

DOI10.1155/2018/3626543zbMath1427.35157OpenAlexW2787954773MaRDI QIDQ1720790

Nguyen Thanh Long, Le Thi Phuong Ngoc, Nguyen Huu Nhan

Publication date: 8 February 2019

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/3626543

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Integro-partial differential equations (35R09)

Related Items (3)

Exact Number of Positive Solutions for the Kirchhoff Equation ⋮ Multiplicity and concentration of positive solutions for \((p, q)\)-Kirchhoff type problems ⋮ Normalized solutions for the Kirchhoff equation on noncompact metric graphs ^*

Cites Work

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• On a nonlinear wave equation with boundary conditions of two-point type
• 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
• Existence and exponential decay for a Kirchhoff-Carrier model with viscosity
• On global solvability and asymptotic behaviour of a mixed problem for a nonlinear degenerate Kirchhoff model in moving domains
• 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
• Existence and asymptotic expansion of the weak solution for a wave equation with nonlinear source containing nonlocal term
• A Robin-Dirichlet problem for a nonlinear wave equation with the source term containing a nonlinear integral
• 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
• Existence and asymptotic behaviour for a degenerate Kirchhoff-Carrier model with viscosity and nonlinear boundary conditions
• Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation

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