Wave equations with super-critical interior and boundary nonlinearities

DOI10.1016/j.matcom.2011.04.006zbMath1248.35128OpenAlexW2029169301MaRDI QIDQ435810

Lorena Bociu, Daniel Toundykov, Mohammad A. Rammaha

Publication date: 12 July 2012

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2011.04.006

zbMATH Keywords

nonlinear dampingenergy decaysuper-critical source

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order semilinear hyperbolic equations (35L71)

Related Items (8)

Blow-up of positive initial energy solutions for a system of nonlinear wave equations with supercritical sources ⋮ Variational approach to stability of semilinear wave equation with nonlinear boundary conditions ⋮ Hyperbolic relaxation of reaction-diffusion equations with dynamic boundary conditions ⋮ Blow-up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities ⋮ Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping ⋮ Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level ⋮ Global existence and blow-up of solution for the semilinear wave equation with interior and boundary source terms ⋮ Variational analysis of semilinear plate equation with free boundary conditions

Cites Work

• Local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping
• On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms
• Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems
• Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction
• Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping
• Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping
• Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions
• Das Anfangswertproblem im Großen für eine Klasse nichtlinearer Wellengleichungen
• Sharp regularity theory for second order hyperbolic equations of Neumann type. I: \(L_ 2\) nonhomogeneous data
• Regularity theory of hyperbolic equations with non-homogeneous Neumann boundary conditions. II: General boundary data
• Saddle points and instability of nonlinear hyperbolic equations
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• Trace regularity of the solutions of the wave equation with homogeneous Neumann boundary conditions and data supported away from the boundary
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Existence for a nonlinear wave equation with damping and source terms.
• Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term
• Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms
• Mixed problems for hyperbolic equations. I: Energy inequalities
• Non-linear semi-groups
• Global existence for the wave equation with nonlinear boundary damping and source terms
• Mathematical Control Theory of Coupled PDEs
• On a wave equation with supercritical interior and boundary sources and damping terms
• A trace theorem for solutions of the wave equation, and the remote determination of acoustic sources
• Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping
• Optimality of Energy Estimates for the Wave Equation with Nonlinear Boundary Velocity Feedbacks
• On nonlinear wave equations with degenerate damping and source terms
• ON THE ATTRACTOR FOR A SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENT AND NONLINEAR BOUNDARY DISSIPATION
• Existence and asymptotic stability for the semilinear wave equation with boundary damping and source term
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Wave equations with super-critical interior and boundary nonlinearities