Electron. J. Diff. Eqns., Vol. 2007(2007), No. 41, pp. 1-29.

Generalized solutions to linearized equations of thermoelastic solid and viscous thermofluid

Anvarbek M. Meirmanov, Sergey A. Sazhenkov

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.

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Anvarbek M. Meirmanov
Center for Advanced Mathematics and Physics
National University of Sciences and Technology
Peshawar Road, Rawalpindi 46000, Pakistan.
Mathematical Department, Belgorod State University
Ul. Pobedy 85, Belgorod 308015, Russia
email: anvarbek@list.ru
Sergey A. Sazhenkov
Center for Advanced Mathematics and Physics
National University of Sciences and Technology
Peshawar Road, Rawalpindi 46000, Pakistan.
Institute of Hydrodynamics
Siberian Division of Russian Academy of Sciences
Prosp. Lavrentieva 15, Novosibirsk 630090, Russia
email:sazhenkovs@yahoo.com   http://sazhenkovs.narod.ru/Serezha.html

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