Andrey ZVYAGIN - Solvability of thermoviscoelastic non-Newtonian models
I2M - Château-Gombert
39 rue Frédéric Joliot-Curie
13453 MARSEILLE cedex 13
Andrey ZVYAGIN (Voronezh State University, Russian Federation)
The initial–boundary value problems under consideration describe the weakly concentrated water polymer solutions motion. In particular, Voigt model, Kelvin–Voigt model, the second grade order model will be considered. In this mathematical models the viscosity depends on a temperature, which leads to the emergence of additional heat balance equation (it is a parabolic equation with nonsmooth coefficients and with the right part from L1(0,T ;L1(Ω)). For these initial–boundary value problems under consideration the existence theorems of weak solutions will be proved. For this the topological approximation approach for hydrodynamic problems is used.