Abstract
In this paper, using mappings of the involution type, we introduce a nonlocal analogue of the two- dimensional Laplace operator and consider the corresponding two-dimensional differential equation of parabolic type with involution. For this equation, the direct and inverse problems of finding the factors of the right-hand side, depending on the spatial variables, are studied. The studied problems are solved by reducing them to direct and inverse problems for classical two-dimensional differential equations of parabolic type. On the basis of well-known theorems ob- tained for auxiliary problems, theorems on the existence and uniqueness of the solution of the studied problems are proved. The explicit form of solutions of the studied problems is constructed in the form of a series.