Nonlocal Boundary Value Problems for Elliptic-Parabolic Differential and Difference Equations

Abstract EN

The abstract nonlocal boundary value problem -d2u(t)/dt2+Au(t)=g(t),0

The well-posedness of this problem in Hölder spaces with a weight is established.

The coercivity inequalities for the solution of boundary value problems for elliptic-parabolic equations are obtained.

The first order of accuracy difference scheme for the approximate solution of this nonlocal boundary value problem is presented.

The well-posedness of this difference scheme in Hölder spaces is established.

In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained.