Dirichlet Problem for a fourth-order equation

Abstract

In a rectangular domain on the plane, we consider the Dirichlet problem for a fourthorder pseudoparabolic equation with double differentiation with respect to each of the variables. To solve the problem, we reduce it to a system of Fredholm equations, whose solvability is established under additional conditions on the coefficients of the equation by the method of a priori estimates. © 2011 Pleiades Publishing, Ltd.