In the present paper the boundary value problem for the Sobolev type equation{∂∂tL(u(t,x))+M(u(t,x))=f(t,x),t>0, x=(x1,…,xn)∈Ω⊂Rn,u|∂Ω=0,(Lu)(0,x)=g(z),x∈Ω,
is considered, where L and M are second-order differential operators. It is proved that under some conditions this problem in the corresponding space has the unique solution.