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.
Show me the
PDF file (422K),
TEX file, and other files for this article.
 |
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
|
|---|
Return to the EJDE web page