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We consider a mathematical model which describes the quasistatic transmission problem in thermo-viscoplasticity. We derive a weak formulation of the system of motion equation and energy equation. We prove the existence and uniqueness of the solution and some properties of the solution. [ABSTRACT FROM AUTHOR]

We consider a mathematical model which describes the steadystate flow of a Herschel-Bulkley fluid whose the consistency and the yield limit depend on the temperature and with mixed boundary conditions, including a frictional boundary condition. We derive a weak formulation of the coupled system of motion and energy equations which consists of a variational inequality for the velocity field. We prove the existence of weak solutions. In the asymptotic limit case of a high thermal conductivity, the temperature becomes a constant solving an implicit total energy equation involving the consistency function and the yield limit. [ABSTRACT FROM AUTHOR]

We consider a mathematical model that describes the dynamic evolution of damage in elastic-thermo-viscoplastic materials with displacementtraction, and Neumann and Fourier boundary conditions. We derive a weak formulation of the system consisting of a motion equation, an energy equation, and an evolution damage inclusion. This system has an integro-differential variational equation for the displacement and the stress fields, and a variational inequality for the damage field. We prove existence and uniqueness of the solution, and the positivity of the temperature. [ABSTRACT FROM AUTHOR]