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Mathematical analysis of thermoplasticity with linear kinematic hardening

100%

Chełmiński K. , Racke R.

tom Vol. 12, nr 1

37-57

We study thermoplasticity with the Prandtl-Reuss flow rule and with a linear evolution equation for the kinematic hardening. The yield function associated with the system under consideration depends explicitly on the temperature. To have a control on the temperature, we slightly modify the heat equation and prove that an approximation process, based on the Yosida approximation, converges to a global in time solution of the (modified) system of thermoplasticity.

Qualitative aspects of solutions in resonators

100%

Quintanilla R. , Racke R.

Archives of Mechanics

2008

tom Vol. 60, nr 4

345-360

We consider the system of micro-beam resonators in the thermoelastic theory of Lord and Shulmann. First, we prove the uniqueness and instability of solutions when the sign of a parameter is not prescribed. Existence of solutions and uniform bounds for the real part of the spectrum have been found. We finish the paper by proving the impossibility of the time localization of solutions.