Global existence and minimal decay regularity for the Timoshenko system: the case of non-equal wave speeds

DOI10.1016/j.jde.2015.06.041zbMath1348.35136arXiv1503.06291OpenAlexW2963121541MaRDI QIDQ496710

Shuichi Kawashima, Naofumi Mori, Jiang Xu

Publication date: 22 September 2015

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

Full work available at URL: https://arxiv.org/abs/1503.06291

zbMATH Keywords

critical Besov spaceshigh-frequency and low-frequency decompositionloss of regularity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Thermal effects in solid mechanics (74F05) Long-time behavior of solutions for dynamical problems in solid mechanics (74H40) Initial value problems for first-order hyperbolic systems (35L45) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Related Items (12)

Global existence for the Jordan-Moore-Gibson-Thompson equation in Besov spaces ⋮ An S \& K mixed condition for symmetric hyperbolic systems with non-symmetric relaxations ⋮ Global existence and large-time behavior of smooth solutions to the Timoshenko-Fourier system in thermoelasticity ⋮ Stability for a Coupled System of Second-Order Evolution Equations with Indirect Memory-Damping ⋮ The optimal time‐decay estimate of solutions to two‐fluid Euler‐Maxwell equations in the critical Besov space ⋮ Well-posedness and decay property for the Cauchy problem of the standard linear solid model with thermoelasticity of type III ⋮ Decay property for solutions to plate type equations with variable coefficients ⋮ Global existence and decay estimates for the solution of a nonlinear Bresse system ⋮ Global well-posedness and polynomial decay for a nonlinear Timoshenko-Cattaneo system under minimal Sobolev regularity ⋮ Well-posedness and decay property of regularity-loss type for the Cauchy problem of the standard linear solid model with Gurtin–Pipkin thermal law ⋮ Dissipative structure and global existence in critical space for Timoshenko system of memory type ⋮ Stability for locally coupled wave-type systems with indirect mixed-type dampings

Cites Work

• Unnamed Item
• Global solutions to the 3-D incompressible inhomogeneous Navier-Stokes system
• The optimal decay estimates on the framework of Besov spaces for generally dissipative systems
• The stability number of the Timoshenko system with second sound
• Existence of global strong solutions in critical spaces for barotropic viscous fluids
• \(L^p - L^q - L^r\) estimates and minimal decay regularity for compressible Euler-Maxwell equations
• Compressible fluid flow and systems of conservation laws in several space variables
• Relaxation-time limits of non-isentropic hydrodynamic models for semiconductors
• Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces
• On the well-posedness of the incompressible density-dependent Euler equations in the \(L^p\) framework
• Uniform stabilization for the transmission problem of the Timoshenko system with memory
• On the stability of damped Timoshenko systems: Cattaneo versus Fourier law
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Energy decay for Timoshenko systems of memory type.
• Global stability for damped Timoshenko systems
• Global existence in critical spaces for compressible Navier-Stokes equations
• Mildly dissipative nonlinear Timoshenko systems -- global existence and exponential stability.
• Local well-posedness for the incompressible Euler equations in the critical Besov spaces.
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• Relaxation limit in Besov spaces for compressible Euler equations
• Global existence and optimal decay rates for the Timoshenko system: the case of equal wave speeds
• On the wellposedness of three-dimensional inhomogeneous Navier-Stokes equations in the critical spaces
• A transmission problem for the Timoshenko system
• Global classical solutions for partially dissipative hyperbolic system of balance laws
• Navier-Stokes equation with variable density and viscosity in critical space
• Exponential stability for the Timoshenko system with two weak dampings
• Fourier Analysis and Nonlinear Partial Differential Equations
• Decay property of Timoshenko system in thermoelasticity
• DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION
• DECAY PROPERTY OF REGULARITY-LOSS TYPE FOR DISSIPATIVE TIMOSHENKO SYSTEM
• DECAY PROPERTY OF REGULARITY-LOSS TYPE AND NONLINEAR EFFECTS FOR DISSIPATIVE TIMOSHENKO SYSTEM
• Stabilisation de la poutre de Timoshenko
• Decay rates and global existence for semilinear dissipative Timoshenko systems
• DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH FOURIER'S TYPE HEAT CONDUCTION

This page was built for publication: Global existence and minimal decay regularity for the Timoshenko system: the case of non-equal wave speeds