Method of Construction of Finite Integral Transform for Operator of Parabolic Differential Equation under Mixed Boundary Conditions

The method of construction of non-classical finite integral transforms for the operator of parabolic differential equation under conditions of the first kind on the sought function on the upper layer boundary and of the second kind on the lower one on the basis of the expansion by orthogonal eigenfunctions is presented. The Sturm-Liouville problem is solved and its solution is investigated. Linearization of the characteristic equation is considered. The influence of the coefficient of advective transfer velocity on the inverse integral transform is studied. The eigenvalues of the Sturm-Liouville problem are investigated.