On an initial boundary value problem for nonlinear pseudoparabolic equation with two space variables

Abstract

In this paper, an initial-boundary value problem of Riemann Ililbcrt type for both linear and nonlinear pseudoparabolic equations in complex form are investigated. In the linear ease, by means of the successive approximation method, the problem is solved by reducing it to an elliptic problem and an estimate for the solution is derived. No restrictions on the smallness of coefficients are needed in the argument. In the nonlinear case, the problem is solved by the embedding and Newton's method. Finally the error estimates for the approximate solutions are provided.