Abstract
We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic‐parabolic equation with the nonlocal boundary condition. Well‐posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic‐parabolic differential equations are obtained.
Highlights
Allaberen Ashyralyev and Okan GercekAcademic Editor: Ravshan Ashurov Copyright q 2012 A
Methods of solutions of nonlocal boundary value problems for mixed-type differential equations have been studied extensively by various researchers see, e.g., 1–19 and the references therein .In 20, we considered the well-posedness of the following multipoint nonlocal boundary value problem: − d2u t dt[2]Au t gt, 0≤t≤1, du t dt − Au t f t,−1 ≤ t ≤ 0, J u1 αiu λi φ, i1−1 ≤ λ1 < λ2 < · · · < λi < · · · < λJ ≤ 0, Abstract and Applied Analysis in a Hilbert space H with the self-adjoint positive definite operator A under assumption |αi| ≤ 1.The well-posedness of multipoint nonlocal boundary value problem 1.1 in Holder spaces with a weight was established
We study well-posedness of problem 1.3
Summary
Academic Editor: Ravshan Ashurov Copyright q 2012 A. We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. Coercivity estimates in Holder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained
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