Existence of periodic solutions for the quasi-static thermoelastic thermistor problem (Q1021414)

The author consider a model for thermistor problem which consists of a nonlinear coupled system of partial differential equations which includes the evolution equation of the temperature in a conductor body, the stationary charge conservation equation of electrical current and a system of quasi-static linear thermoelasticity equations of displacements subject to the external forces and heat sources. For this quasi-static thermoelastic thermistor problem, the author establish the existence of weak periodic solutions. To this end, it is rewritten the system of equations as an abstract problem in order to utilize the maximal monotone mappings theory and a fixed point argument for a suitable operator equation.