α=1 iα (D). Here Cα1+α2+···+αn stands for the class of all functions which are continuous in D together with their derivatives ∂r1+r2+···+rn/∂xr1 1 ∂x r2 2 . . . ∂x rn n (r1 = 0, . . . , α1, r2 = 0, . . . , α2, . . . , rn = 0, . . . , αn). One can treat equation (1) as the most general pseudo-parabolic equation. Its special cases are investigated in [1], [2] (p. 5). One can meet several versions of equation (1) in applications, for instance, the Boussinesq–Love equation in the theory of oscillations (see [1], formula (20)) and the Aller equation ([2], p. 261) in the mathematical modeling of the moisture absorption in biology. A solution to the Goursat problem (Γ) for equation (1) is obtained [3] in the domain D = {x10 < x1 < x11, x20 < x2 < x21, . . . , xn0 < xn < xn1} with the boundary values ∂i1u ∂x1 1 (x10, x2, . . . , xn) = φ1i1(x2, . . . , xn) (i1 = 0,m1 − 1), ∂i2u ∂x2 2 (x1, x20, . . . , xn) = φ2i2(x1, x3, . . . , xn) (i2 = 0,m2 − 1), (2)