Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 904824, 16 pages
doi:10.1155/2008/904824

Nonlocal boundary value problems for elliptic-parabolic differential and difference equations

Abstract

The abstract nonlocal boundary value problem -d2u(t)/dt2+Au(t)=g(t),0<t<1,du(t)/dt-Au(t)=f(t),1<t<0,u(1)=u(-1)+μ for differential equations in a Hilbert space H with the self-adjoint positive definite operator A is considered. 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.