On the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and source

DOI10.1007/s00205-016-1055-2zbMath1368.35166arXiv1506.00910OpenAlexW3103179436MaRDI QIDQ509956

Enzo Vitillaro

Publication date: 16 February 2017

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.00910

zbMATH Keywords

local Hadamard well-posednesssupercritical boundary damping

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order hyperbolic equations (35L20) Wave equation (35L05) Blow-up in context of PDEs (35B44)

Related Items (16)

Blow-up problems for a parabolic equation coupled with superlinear source and local linear boundary dissipation ⋮ Full discretization error analysis of exponential integrators for semilinear wave equations ⋮ On the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and supercritical sources ⋮ Blow-up theorems for a structural acoustics model ⋮ Generalized Wentzell boundary conditions and quantum field theory ⋮ Splitting schemes for the semi-linear wave equation with dynamic boundary conditions ⋮ Finite element discretization of semilinear acoustic wave equations with kinetic boundary conditions ⋮ On a variational problem for a model of a Stieltjes string with a backlash at the end ⋮ Control of blowup and approximate optimality conditions for the wave equations ⋮ Approximation by regular functions in Sobolev spaces arising from doubly elliptic problems ⋮ Global solutions and blow-up for the wave equation with variable coefficients. I: Interior supercritical source ⋮ Global well-posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping, linear strong damping and logarithmic nonlinearity ⋮ Dynamical behaviors of solutions to nonlinear wave equations with vanishing local damping and Wentzell boundary conditions ⋮ Uniform stabilization of semilinear wave equations with localized internal damping and dynamic Wentzell boundary conditions with a memory term ⋮ Blow-up for the wave equation with hyperbolic dynamical boundary conditions, interior and boundary nonlinear damping and sources ⋮ A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions

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