In my talk I shall review recent results obtained in 2 papers, First one in collaboration with M. Fuest, K.Hajduk and M. Sierzega and a second one with P. Bies. I'm going to show a recently found functional inequality, which seems promising when dealing with systems of PDEs via the Fisher information method. In particular, I will show a result obtained with P.Bies, stating global-in-time existence of unique regular solutions to the system describing the evolution of the heated string. It is a thermodynamically consistent combination of two very classical equations: heat equation and string equation. Moreover, it's a particular example of the basic problem of thermoelasticity. Still, till our result the question of global existence was opened. Finally, at the end I will mention a recent result applying our method to the 1D combustion problem, a different area of mathematical physics.