Existence and exponential decay of the Dirichlet problem for a nonlinear wave equation with the Balakrishnan-Taylor term

DOI10.1007/s10986-020-09469-7zbMath1442.35243OpenAlexW3005886994WikidataQ115603600 ScholiaQ115603600MaRDI QIDQ779827

Bui Duc Nam, Nguyen Huu Nhan, Le Thi Phuong Ngoc, Nguyen Thanh Long

Publication date: 14 July 2020

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-020-09469-7

zbMATH Keywords

local existencelinearization methodexponential decayFaedo-Galerkin methodLiapunov finctional

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) PDEs in connection with mechanics of deformable solids (35Q74) Second-order semilinear hyperbolic equations (35L71)

Cites Work

• General decay rate estimates for viscoelastic wave equation with Balakrishnan-Taylor damping
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• General decay for a viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping, dynamic boundary conditions and a time-varying delay term
• Finite-dimensional attractors for the Kirchhoff equation with a strong dissipation
• Long-time dynamics of Kirchhoff wave models with strong nonlinear damping
• Asymptotic behavior of a nonlinear Kirchhoff type equation with spring boundary conditions
• On a nonlinear Kirchhoff-Carrier wave equation associated with Robin conditions
• Existence and exponential decay for a Kirchhoff-Carrier model with viscosity
• On global solutions and blow-up solutions of nonlinear Kirchhoff strings with nonlinear dissipation
• On the viscoelastic equation with Balakrishnan-Taylor damping and acoustic boundary conditions
• Stabilization for the wave equation with variable coefficients and Balakrishnan-Taylor damping
• Stabilization for wave equation of variable coefficients with Balakrishnan-Taylor damping and source term
• General decay rate for weak viscoelastic wave equation with Balakrishnan-Taylor damping and time-varying delay
• On a system of nonlinear wave equations with Balakrishnan-Taylor damping
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