The Riemann Function for the Third-Order One-Dimensional Pseudoparabolic Equation

In this work, some classes of initial boundary-value problems are investigated in the Sobolev space for the third-order linear pseudoparabolic equation having, in general, nonsmooth coefficients. A new type of Riemann function concept is given for these problems, which is more natural than the classical Riemann-type function concept, and an integral form of the solutions of nonhomogeneous problems can be found more naturally using this concept.