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- Publications
- Influence

On the Stability of Damped Timoshenko Systems: Cattaneo Versus Fourier Law

- Hugo D. Fernández Sare, R. Racke
- Mathematics
- 26 February 2009

We consider hyperbolic Timoshenko-type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. While exponential stability under the… Expand

Timoshenko systems with indefinite damping

Abstract We consider the Timoshenko system in a bounded domain ( 0 , L ) ⊂ R 1 . The system has an indefinite damping mechanism, i.e. with a damping function a = a ( x ) possibly changing sign,… Expand

Lectures on nonlinear evolution equations

- R. Racke
- Mathematics
- 1992

Introduction.- 1. Global solutions to wave equations - existence theorems.- 2. L^p - L^q-decay estimates for the linear we equation.- 3. Linear symmetric hyperbolic systems.- 3.1 Energy estimates.-… Expand

Global stability of large solutions to the 3D Navier-Stokes equations

- G. Ponce, R. Racke, T. Sideris, E. Titi
- Mathematics
- 1994

We prove the stability of mildly decaying global strong solutions to the Navier-Stokes equations in three space dimensions. Combined with previous results on the global existence of large solutions… Expand

Asymptotic behavior of solutions in linear 2- or 3-d thermoelasticity with second sound

- R. Racke
- Mathematics
- 1 June 2003

We consider thermoelastic systems in two or three space dimensions where thermal disturbances are modeled propagating as wavelike pulses traveling at finite speed. This is done using Cattaneo's law… Expand

Thermoelasticity with second sound—exponential stability in linear and non‐linear 1‐d

- R. Racke
- Mathematics
- 25 March 2002

We consider linear and non-linear thermoelastic systems in one space dimension where thermal disturbances are modelled propagating as wave-like pulses travelling at finite speed. This removal of the… Expand

Energy decay for Timoshenko systems of memory type

- F. Ammar-Khodja, A. Benabdallah, J. Rivera, R. Racke
- Mathematics
- 10 October 2003

Abstract Linear systems of Timoshenko type equations for beams including a memory term are studied. The exponential decay is proved for exponential kernels, while polynomial kernels are shown to lead… Expand

Ill-posed problems in thermomechanics

- M. Dreher, R. Quintanilla, R. Racke
- Mathematics, Computer Science
- Appl. Math. Lett.
- 1 September 2009

Abstract Several thermomechanical models have been proposed from a heuristic point of view. A mathematical analysis should help to clarify the applicability of these models, among those recent… Expand

A note on stability in three-phase-lag heat conduction

- R. Quintanilla, R. Racke
- Physics
- 2008

In this note we consider two cases in the theory of the heat conduction models with three-phase-lag. For each one we propose a suitable Lyapunov function. These functions are relevant tools which… Expand

Asymptotic stability and global existence in thermoelasticity with symmetry

First we prove an exponential decay result for solutions of the equations of linear, homogeneous, isotropic thermoelasticity in bounded regions in two or three space dimensions if the rotation of the… Expand