Well-posedness for a class of Kirchhoff equations with damping and memory terms

DOI10.1093/IMAMAT/HXV018zbMath1338.35420OpenAlexW1899303571MaRDI QIDQ2802156

Gongwei Liu, Hua Chen

Publication date: 25 April 2016

Published in: IMA Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imamat/hxv018

zbMATH Keywords

global existenceKirchhoff equationblow upexponential growthexponential decay

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Nonlinear constitutive equations for materials with memory (74D10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with mechanics of deformable solids (35Q74) Blow-up in context of PDEs (35B44) Integro-partial differential equations (35R09)

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The family of random attractors for nonautonomous stochastic higher-order Kirchhoff equations with variable coefficients ⋮ Dynamics of nonlinear hyperbolic equations of Kirchhoff type ⋮ Blow-up of solutions to a class of Kirchhoff equations with strong damping and nonlinear dissipation ⋮ Global nonexistence for a nonlinear viscoelastic equation with nonlinear damping and velocity-dependent material density ⋮ Blow-up of solutions for a wave equation with nonlinear averaged damping and nonlocal nonlinear source terms ⋮ Nonlinear wave equation with both strongly and weakly damped terms: supercritical initial energy finite time blow up ⋮ Upper and lower bounds of blowup time to a strongly damped wave equation of Kirchhoff type with memory term and nonlinear dissipations

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