Takhirov Zh. O.
Ukr. Mat. Zh. - 2017. - 69, № 12. - pp. 1690-1700
We consider a problem with free boundary for systems of quasilinear parabolic equations. A part of the boundary conditions are given in the nonlocal form. The a priori estimates of the H¨older norms are established. These estimates are used to prove the existence and uniqueness of the solution.
Ukr. Mat. Zh. - 2012. - 64, № 1. - pp. 71-80
We investigate the one-phase Florin problem for a parabolic equation with nonlocal condition. Theorems one the existence and uniqueness of a solution are proved, and a priori estimates for the solution are obtained.