Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain
We establish the convergence of the Rothe method for a parabolic equation with nonlocal boundary conditions and obtain an a priori estimate for the constructed difference scheme in the grid norm on a ball. We prove that the suggested iterative process for the solution of the posed problem converges in the small.
English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 2, pp 269-280.
Citation Example: Berezovsky A. A., Mitropolskiy Yu. A., Shkhanukov-Lafishev M. Kh. Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain // Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 244–254.