Constructive Function Theoretic Methods for Higher Order Pseudoparabolic Equations.

摘要

In this paper the approach to higher order,elliptic partial differential equations in the plane is extended to the cases of meta and pseudoparabolic equations. The method makes use of a generalization of the Riemann function associated with the complex hyperbolic equation obtained by analytic continuation. A fundamental solution is obtained whose Taylor (Laurent) expansion in powers of the time has as its first term the classical fundamental solution of Vekua. Integral representations are obtained for the initial boundary value problems.