On pseudoparabolic equations and their approximation by parabolic equations

Abstract

Pseudoparabolic partial differential equations (of composite type and of third order) has been used for the approximation of solutions of the parabolic equation M0[u]=0, and vice versa. We refer e.g. to the work of Ewing2, who considered the improperly posed backward time problem for the parabolic equation and its approximation by the properly posed initial value problem for the pseudoparabolic equation. This motivates our recent study of the solution to the equation (1) and their approximation for small parameters p. Our approach is a generalization of the method of complex integral operators due to S. Bergman and I. N. Vekua.