Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 41, pp. 1-29.

Title: Generalized solutions to linearized equations of thermoelastic
       solid and viscous thermofluid

Authors: Anvarbek M. Meirmanov (National Univ., Rawalpindi, Pakistan)
         Sergey A. Sazhenkov   (National Univ., Rawalpindi, Pakistan)
 
Abstract:
 Within the framework of continuum mechanics, the full description
 of joint motion of elastic bodies and compressible viscous fluids
 with taking into account thermal effects is given by the system
 consisting of the mass, momentum, and energy balance equations,
 the first and the second laws of thermodynamics, and an additional
 set of thermomechanical state laws. The present paper is devoted
 to the investigation of this system. Assuming that variations of
 the physical characteristics of the thermomechanical system of the
 fluid and the solid are small about some rest state, we derive the
 linearized non-stationary dynamical model, prove its
 well-posedness, establish additional refined global integral
 bounds for solutions, and further deduce the linearized
 incompressible models and models incorporating absolutely rigid
 skeleton, as asymptotic limits.
  
Submitted July 20, 2006. Published March 9, 2007.
Math Subject Classifications: 35D05, 35Q30, 74A10, 80A17, 93B18.
Key Words: Thermoelastic solid; viscous thermofluid;
    compressibility; linearization; existence and uniqueness theory;
    weak generalized solutions.