A nonclassical nonlinear boundary value problem for parabolic pseudodifferential equations in the
Sobolev spaces is considered. The problem is reduced to a boundary value problem for an elliptic equation
by applying the Laplace Transforms. The existence of a solution is proved by using the Schauder theorem.
The Laplace transform is used to solve parabolic pseudodifferential equations in the Sobolev spaces. The
proof is substantially simplified by applying the Schauder theorem.
