RETRACTED ARTICLE: Global existence and general decay estimates of solutions of the degenerate or non-degenerate Kirchhoff equation with general dissipation

DOI10.1007/s00028-010-0076-9zbMath1372.35176OpenAlexW1993445569MaRDI QIDQ657019

Abbes Benaissa, Aissa Guesmia

Publication date: 13 January 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-010-0076-9

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (2)

Well-posedness and direct internal stability of coupled non-degenerate Kirchhoff system via heat conduction ⋮ On wave equation: review and recent results

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global existence and energy decay of solutions for Kirchhoff-Carrier equations with weakly nonlinear dissipation
• Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems
• Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction
• Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations
• Regularity of higher energies of wave equation with nonlinear localized damping and a nonlinear source
• Energy decay of solutions of a degenerate Kirchhoff equation with a weak nonlinear dissipation
• Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions
• Global solvability for the degenerate Kirchhoff equation with real analytic data
• A difference inequality and its application to nonlinear evolution equations
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• Nonlinear Goursat problem in Gevrey spaces for generalized Kirchhoff equations
• Global solvability for the generalized degenerate Kirchhoff equation with real-analytic data in \(\mathbb{R}^n\)
• On global solutions and blow-up solutions of nonlinear Kirchhoff strings with nonlinear dissipation
• Existence for a nonlinear wave equation with damping and source terms.
• Global existence and energy decay of solutions to the Cauchy problem for a wave equation with a weakly nonlinear dissipation
• Decay rates for dissipative wave equations
• Global existence for abstract evolution equations of weakly hyperbolic type
• Weakly hyperbolic equation with fast oscillating coefficients
• A quasilinear integrodifferential equation of hyperbolic type
• Decay rates for solutions of a Maxwell system with nonlinear boundary damping
• Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms
• On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms
• On continuity of functions with values in various Banach spaces
• Mathematical Control Theory of Coupled PDEs
• Local solutions for a nonlinear degenerate Hyperbolic equation
• Some nonlinear degenerate wave equations
• A new method to obtain decay rate estimates for dissipative systems
• On local solutions of some mildly degenerate hyperbolic equations
• On the mildly degenerate Kirchhoff string
• Global solvability and uniform decays of solutions to quaslinear equation with nonlinear boundary dissipation

This page was built for publication: RETRACTED ARTICLE: Global existence and general decay estimates of solutions of the degenerate or non-degenerate Kirchhoff equation with general dissipation