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.

An interesting and useful analogy can be drawn between the equations of static poroelasticity and the equations of thermoelasticity including entropy. The correspondence is of practical use in determining the effective parameters in an inhomogeneous poroelastic medium using known results from the literature on the effective thermal expansion coefficient and the effective heat capacity of a diso...

A two dimensional generalized thermoelastic problem of a thick circular plate of finite thickness and infinite extent subjected to continuous axisymmetric heat supply and an internal heat generation is studied within the context of generalized thermoelasticity. Unified system of equations for classical coupled thermoelasticity, Lord-Shulman and Green-Lindsay theory is considered. An exact solut...

Using multipler techniques and Lyapunov methods, we derive explicit decay rates for the energy in the higher-dimensional system of thermoelasticity with a nonlinear velocity feedback on part of the boundary of a thermoelastic body, which is clamped along the rest of its boundary.

The hysteretic behavior of many-particle systems with non-convex free energy can be modeled by nonlocal Fokker-Planck equations that involve two small parameters and are driven by a timedependent constraint. In this paper we consider the fast reaction regime related to Kramers-type phase transitions and prove that the dynamics in the small-parameter limit can be described by a rate-independent ...