منابع مشابه
Slow Decay in Linear Thermo-elasticity
Energy estimates show that linearized thermo-elasticity deenes a contraction semi-group on a Hilbert space. We show that under a geometric condition this contraction is not strict, or, more precisely, the norm of the semi group is 1 for all t 0. Convex domains always satisfy the geometric condition. 2. introduction Let R n be a bounded domain with smooth boundary ?. We consider the problem @ 2 ...
متن کاملSpatial stability in linear thermoelasticity
Uniqueness and spatial stability are investigated for smooth solutions to boundary value problems in non-classical linearised and linear thermoelasticity subject to certain conditions on material coefficients. Uniqueness is derived for standard boundary conditions on bounded regions using a generalisation of Kirchhoff’s method. Spatial stability is discussed for the semi-infinite prismatic cyli...
متن کاملOn (non-)exponential decay in generalized thermoelasticity with two temperatures
We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential stability for the Lord-Shulman model.
متن کاملExponential Decay in Nonsimple Thermoelasticity of Type Iii
This paper deals with the model proposed for nonsimple materials with heat conduction of type III. We analyze first the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.
متن کاملOn thermodynamic potentials in linear thermoelasticity
The four thermodynamic potentials, the internal energy u 1⁄4 uð ij; sÞ, the Helmholtz free energy f 1⁄4 f ð ij; T Þ, the Gibbs energy g 1⁄4 gðrij; T Þ and the enthalpy h 1⁄4 hðrij; sÞ are derived, independently of each other, by using the Duhamel–Neumann extension of Hooke’s law and an assumed linear dependence of the specific heat on temperature. A systematic procedure is then presented to exp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 2000
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/1788420