We study a nonlocal parabolic problem modeling the temperature in a thin region during linear friction welding for a hard material. We derive the structures of steady states of this nonlocal problem and its associated approximated problems. Moreover, some remarks on the parabolic problem are given.
"A nonlocal parabolic problem arising in linear friction welding." Osaka J. Math. 47 (1) 33 - 40, March 2010.