Weighted integral inequality and applications in general energy decay estimate for a variable density wave equation with memory

DOI10.1186/s13661-018-1085-9zbMath1499.35073OpenAlexW2898689168WikidataQ129021847 ScholiaQ129021847MaRDI QIDQ2126488

Fengying Hu, Fu Shan Li

Publication date: 19 April 2022

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-018-1085-9

zbMATH Keywords

memory kernelviscoelastic equationweighted integral inequalitygeneral decay estimate

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Linear higher-order PDEs (35G05) Initial value problems for higher-order hyperbolic equations (35L30) Initial-boundary value problems for linear higher-order PDEs (35G16)

Related Items

Asymptotic Stability for a Quasilinear Viscoelastic Equation with Nonlinear Damping and Memory ⋮ The refinement and generalization of Hardy's inequality in Sobolev space ⋮ DYNAMIC PROPERTIES FOR NONLINEAR VISCOELASTIC KIRCHHOFF-TYPE EQUATION WITH ACOUSTIC CONTROL BOUNDARY CONDITIONS Ⅱ ⋮ Global existence and stability of a class of nonlinear evolution equations with hereditary memory and variable density

Cites Work

• Unnamed Item
• Unnamed Item
• Hitchhiker's guide to the fractional Sobolev spaces
• Global existence and blow-up phenomena for \(p\)-Laplacian heat equation with inhomogeneous Neumann boundary conditions
• General and optimal decay for a quasilinear viscoelastic equation
• Intrinsic decay rates for the energy of a nonlinear viscoelastic equation modeling the vibrations of thin rods with variable density
• Uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping
• Global existence and blow-up phenomena for nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions
• Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation
• Blow-up of solution for a nonlinear Petrovsky type equation with memory
• General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source
• Limit behavior of the solution to nonlinear viscoelastic Marguerre-von Kármán shallow shell system
• Stability of periodic steady-state solutions to a non-isentropic Euler-Maxwell system
• Stability of steady-state solutions to Navier-Stokes-Poisson systems
• Convergence of a non-isentropic Euler-Poisson system for all time
• Global existence and uniqueness of weak solution to nonlinear viscoelastic full marguerre-von kármán shallow shell equations
• Uniform stability of the solution for a memory-type elasticity system with nonhomogeneous boundary control condition
• A general stability result for a quasilinear wave equation with memory
• Exponential and polynomial decay for a quasilinear viscoelastic equation
• Decay estimates for second order evolution equations with memory
• Uniform decay rates for nonlinear viscoelastic Marguerre-von Kármán equations
• Existence and uniform decay for a non-linear viscoelastic equation with strong damping
• GENERAL ENERGY DECAY FOR A DEGENERATE VISCOELASTIC PETROVSKY-TYPE PLATE EQUATION WITH BOUNDARY FEEDBACK
• General decay of energy for a viscoelastic equation with nonlinear damping