On a nonlocal problem for a parabolic equation - Berezansky, Yu. M.; Mitropolskiy, Yu. A.; Shkhanukov-Lafishev, M. Kh. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
We study a nonlocal boundary-value problem for a parabolic equation in a two-dimensional domain, establish ana priori estimate in the energy norm, prove the existence and uniqueness of a generalized solution from the classW 2 1,0 (Q T ), and construct a difference scheme for the second-order approximation.