On existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions

DOI10.1016/S0022-247X(02)00558-9zbMath1026.35084MaRDI QIDQ1399302

Marcelo Moreira Cavalcanti, Juan A. Soriano, Valéria Neves Domingos Cavalcanti

Publication date: 30 July 2003

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

zbMATH Keywords

stabilizationexponential decayglobal solvabilitynonlinear boundary damping

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Degenerate hyperbolic equations (35L80)

Related Items (16)

Exponential boundary stabilization for nonlinear wave equations with localized damping and nonlinear boundary condition ⋮ On totally global solvability of evolutionary equation with unbounded operator ⋮ On totally global solvability of evolutionary equation with monotone nonlinear operator ⋮ Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction ⋮ On a nonlinear wave equation with boundary conditions involved in a Cauchy problem ⋮ The stability for a one-dimensional wave equation with nonlinear uncertainty on the boundary ⋮ Majorant sign of the first order for totally global solvability of a controlled functional operator equation ⋮ Existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary. ⋮ On preservation of global solvability of controlled second kind operator equation ⋮ General decay for a viscoelastic wave equation with density and time delay term in \(\mathbb{R}^n\) ⋮ General energy decay of solutions for a weakly dissipative Kirchhoff equation with nonlinear boundary damping ⋮ Global solutions for a nonlinear hyperbolic equation with boundary memory source term ⋮ Global existence and uniform decay for wave equation with dissipative term and boundary damping ⋮ Well-posedness and uniform decay rates for the Klein–Gordon equation with damping term and acoustic boundary conditions ⋮ A semilinear wave equation with space-time dependent coefficients and a memory boundarylike antiperiodic condition: Regularity and stability ⋮ Global existence and uniform stabilization of a generalized dissipative Klein–Gordon equation type with boundary damping

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Energie decay estimates and exact boundary value controllability for the wave equation in a bounded domain
• Decay of solutions of wave equations in a bounded region with boundary dissipation
• A direct method for the boundary stabilization of the wave equation
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• On the existence and the uniform decay of a hyperbolic equation with nonlinear boundary conditions
• Note on Boundary Stabilization of Wave Equations
• A Note on the Boundary Stabilization of the Wave Equation
• Asymptotic stability and energy decay rates for solutions of hyperbolic equations with boundary damping
• Existence and uniform decay of solutions of a degenerate equation with nonlinear boundary damping and boundary memory source term
• On solvability of solutions of degenerate nonlinear equations on manifolds

This page was built for publication: On existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions