Sharp Decay Rates in Parabolic and Hyperbolic Thermoelasticity
ثبت نشده
چکیده
منابع مشابه
Nonlinear Well-Posedness and Rates of Decay in Thermoelasticitywith Second Sound
We consider the Cauchy problem in nonlinear thermoelasticity with second sound in one space dimension. Due to Cattaneo’s law, replacing Fourier’s law for heat conduction, the system is hyperbolic. We first investigate the local well-posedness as a strictly hyperbolic system, and then discuss the relation between energy estimates for non-symmetric hyperbolic systems and well-posedness. For the g...
متن کاملConditional stability of unstable viscous shock waves in compressible gas dynamics and MHD
Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic–parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small L1 ∩ H3 perturbations, converging time-asymptotically to a translate of...
متن کاملStability of Viscous Shock Profiles for Dissipative Symmetric Hyperbolic-parabolic Systems
Combining pointwise Green’s function bounds obtained in a companion paper [MZ.2] with earlier, spectral stability results obtained in [HuZ], we establish nonlinear orbital stability of small amplitude viscous shock profiles for the class of dissipative symmetric hyperbolic-parabolic systems identified by Kawashima [Kaw], notably including compressible Navier–Stokes equations and the equations o...
متن کاملDiffusion phenomenon in Hilbert spaces and applications
Article history: Received 29 December 2010 Revised 19 January 2011 Available online 4 February 2011 We prove an abstract version of the striking diffusion phenomenon that offers a strong connection between the asymptotic behavior of abstract parabolic and dissipative hyperbolic equations. An important aspect of our approach is that we use in a natural way spectral analysis without involving com...
متن کاملUniqueness and Hölder Type Stability of Continuation for the Linear Thermoelasticity System with Residual Stress
By introducing some auxiliary functions, an elasticity system with thermal effects becomes a coupled hyperbolic-parabolic system. Using this reduced system, we obtain a Carleman estimate with two large parameters for the linear thermoelasticity system with residual stress which is the basic tool for showing stability estimates in the lateral Cauchy problem.
متن کامل