Local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping

DOI10.1016/j.na.2008.11.062zbMath1238.35059OpenAlexW2064936620MaRDI QIDQ419793

Lorena Bociu

Publication date: 20 May 2012

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.2008.11.062

zbMATH Keywords

wave equationlocal existencecritical exponentsnonlinear dampingboundary sourceinterior source

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Second-order nonlinear hyperbolic equations (35L70) Weak solutions to PDEs (35D30)

Related Items (21)

Global existence and decay of energy to systems of wave equations with damping and supercritical sources ⋮ On the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and supercritical sources ⋮ Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources ⋮ Well-posedness of Mindlin-Timoshenko plate with nonlinear boundary damping and sources ⋮ Long-time behavior of a nonlinearly-damped three-layer Rao-Nakra sandwich beam ⋮ Wave equations with super-critical interior and boundary nonlinearities ⋮ Unnamed Item ⋮ Blow-up of positive initial energy solutions for a system of nonlinear wave equations with supercritical sources ⋮ Systems of nonlinear wave equations with damping and supercritical boundary and interior sources ⋮ Global solutions and blow-up for the wave equation with variable coefficients. I: Interior supercritical source ⋮ Strong solutions for semilinear wave equations with damping and source terms ⋮ Hyperbolic relaxation of reaction-diffusion equations with dynamic boundary conditions ⋮ Unnamed Item ⋮ Blow-up result and energy decay rates for binary mixtures of solids with nonlinear damping and source terms ⋮ Quasi-stability and continuity of attractors for nonlinear system of wave equations ⋮ Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping ⋮ Blow-up for the wave equation with hyperbolic dynamical boundary conditions, interior and boundary nonlinear damping and sources ⋮ Hadamard well-posedness for a structure acoustic model with a supercritical source and damping terms ⋮ Blow-up of solutions to systems of nonlinear wave equations with supercritical sources ⋮ On the regularizing effect of nonlinear damping in hyperbolic equations ⋮ Global existence and blow-up of solution for the semilinear wave equation with interior and boundary source terms

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