Hyperbolic-parabolic singular perturbation for nondegenerate Kirchhoff equations with critical weak dissipation

DOI10.1007/s00208-011-0765-xzbMath1259.35016arXiv0901.0185OpenAlexW2070172439MaRDI QIDQ1938415

Marina Ghisi, Massimo Gobbino

Publication date: 4 February 2013

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.0185

zbMATH Keywords

unique global solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Critical exponents in context of PDEs (35B33) Integro-partial differential equations (35R09) Second-order quasilinear hyperbolic equations (35L72)

Related Items (11)

Singular limit problem of abstract second order evolution equations ⋮ Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: decay-error estimates ⋮ Necessary condition on the dissipative term for the asymptotically free property of dissipative Kirchhoff equations ⋮ Existence of solutions for \(p\)-Laplacian parabolic Kirchhoff equation ⋮ The quasilinear parabolic Kirchhoff equation ⋮ An attractor for the singularly perturbed Kirchhoff equation with supercritical nonlinearity ⋮ On a terminal value problem for a system of parabolic equations with nonlinear-nonlocal diffusion terms ⋮ On an initial and final value problem for fractional nonclassical diffusion equations of Kirchhoff type ⋮ The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case ⋮ On the Parabolic Regime of a Hyperbolic Equation with Weak Dissipation: The Coercive Case ⋮ Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perturbations singulières dans les problèmes aux limites et en contrôle optimal
• Scattering and modified scattering for abstract wave equations with time-dependent dissipation
• Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: Time-decay estimates
• Hyperbolic--parabolic singular perturbation for mildly degenerate Kirchhoff equations: Global-in-time error estimates
• Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay
• Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type
• Asymptotic behavior for abstract wave equations with decaying dissipation
• Global-in-time uniform convergence for linear hyperbolic-parabolic singular perturbations
• Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type with weak dissipation
• An Optimal Estimate for the Time Singular Limit of an Abstract Wave Equation
• Hyperbolic-parabolic singular perturbations for scalar nonlinearities
• On some quasilinear wave equations with dissipative terms
• On the mildly degenerate Kirchhoff string
• Singular perturbation hyperbolic-parabolic for degenerate nonlinear equations of Kirchhoff type

This page was built for publication: Hyperbolic-parabolic singular perturbation for nondegenerate Kirchhoff equations with critical weak dissipation