in this paper, we investigate the goursat problem in the class c21(d)cn0 (d  p) c00 (d q)for a third order pseudoparabolic equation. some results are given concerning the existence and uniquenessfor the solution of the suggested problem.

An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed. To construct approximation in time, regularized twolevel schemes are used. The numerical implementation is based on solving the equation with the square root...

We approximate the solution of initial boundary value problems for equations of the form Au′(t) = B(t, u(t)), t ∈ [0, t?]. A is a linear, selfadjoint, positive definite operator on a Hilbert space (H, (·, ·)) and B is a possibly nonlinear operator. We discretize in space by finite element methods and for the time discretization we use explicit linear multistep schemes. We derive optimal order e...

In this paper, we prove the uniqueness of weak solutions for a pseudoparabolic equation modeling two-phase flow in a porous medium, where dynamic effects are included in the capillary pressure.

Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stabl...