Boundary stabilization for wave equations with damping only on the nonlinear Wentzell boundary

DOI10.1016/j.na.2017.08.010zbMath1377.35237OpenAlexW2761429429MaRDI QIDQ1675415

Chan Li, Ti-Jun Xiao, Jin Liang

Publication date: 27 October 2017

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.2017.08.010

zbMATH Keywords

boundary stabilizationdecay ratenonlinear dampingmultidimensional wave equationsWentzell (Ventcel) boundary conditions

Mathematics Subject Classification ID

Control, switches and devices (``smart materials) in solid mechanics (74M05) Stabilization of systems by feedback (93D15) Stability in context of PDEs (35B35) Wave equation (35L05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Membranes (74K15) Nonlinear constitutive equations for materials with memory (74D10) Strings (74K05) PDEs in connection with mechanics of deformable solids (35Q74)

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Asymptotics for wave equations with damping only on the dynamical boundary ⋮ Regularity and stability of wave equations with variable coefficients and Wentzell type boundary conditions ⋮ Uniform stabilization for a string/point mass system via arbitrary local memory effects versus frictional damping ⋮ Stability of the wave equation with localized Kelvin–Voigt damping and dynamic Wentzell boundary conditions with delay ⋮ Uniform decay rate estimates for the 2D wave equation posed in an inhomogeneous medium with exponential growth source term, locally distributed nonlinear dissipation, and dynamic Cauchy–Ventcel–type boundary conditions ⋮ On a variational problem for a model of a Stieltjes string with a backlash at the end ⋮ Long-term dynamical behavior of the wave model with locally distributed frictional and viscoelastic damping ⋮ Asymptotic behaviours of solutions for wave equations with damped Wentzell boundary conditions but no interior damping ⋮ Uniform stabilization for the semilinear wave equation in an inhomogeneous medium with locally distributed nonlinear damping and dynamic Cauchy–Ventcel type boundary conditions ⋮ Dynamical behaviors of solutions to nonlinear wave equations with vanishing local damping and Wentzell boundary conditions

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