On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification (Q1811848)

The author proves in weighted Sobolev spaces the existence, uniqueness, and continuous dependence of the weak solution of three-point boundary value problem for a class of linear and quasilinear parabolic equations with nonlocal condition in a domain with curved boundaries varying with respect to time. To this end the author uses a priori estimates technique. To investigate quasilinear problem the author combines an iterative process with results established for the linear case.