Asymptotic behavior of a class of abstract semilinear integrodifferential equations and applications

DOI10.1006/jmaa.1999.6271zbMath0981.45007OpenAlexW2004881437MaRDI QIDQ1289041

Tiehu Qin

Publication date: 3 March 2002

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

Full work available at URL: https://semanticscholar.org/paper/21e3b9325a04fb2538a94ac5ac4924dfcb352fcc

zbMATH Keywords

Hilbert spacesglobal existenceasymptoticinitial problemsemilinear hyperbolic Volterra integrodifferential equationsviscoelastic dynamics

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Nonlinear constitutive equations for materials with memory (74D10) Asymptotics of solutions to integral equations (45M05) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items (9)

Arbitrary decays for a viscoelastic equation ⋮ Exponential stability for the wave model with localized memory in a past history framework ⋮ A general stability result for the semilinear viscoelastic wave model under localized effects ⋮ Intrinsic decay rate estimates for the wave equation with competing viscoelastic and frictional dissipative effects ⋮ Intrinsic decay rates for the energy of a nonlinear viscoelastic equation modeling the vibrations of thin rods with variable density ⋮ Exponential decay for a quasilinear viscoelastic equation ⋮ Asymptotic stability of the wave equation on compact manifolds and locally distributed viscoelastic dissipation ⋮ Asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel ⋮ Exponential stability for the 2D wave model with localized memory in a past history framework and nonlinearity of arbitrary growth

Cites Work

• Weak solutions of a class of quasilinear hyperbolic integro-differential equations describing viscoelastic materials
• Development of singularities in the motion of materials with fading memory
• Global Existence and Asymptotic Stability for a Semilinear Hyperbolic Volterra Equation with Large Initial Data
• The generalized partial correspondence principle in linear viscoelasticity
• An integro-differential equation with application in heat flow
• A model for one-dimensional, nonlinear viscoelasticity
• An Abstract Second Order Semilinear Volterra Integrodifferential Equation
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