Well- posedness of the Rothe difference scheme for reverse parabolic equations

Subject Areas : Operation Research

Allaberen  Ashyralyev ¹ (Department of Mathematics, Fatih University, Istanbul,34500, Turkey)
Ayfer  Dural ² (Gaziosman Paşa Lisesi Istanbul, Turkey)
Yaşar  Sözen ³ (Department of Mathematics, Fatih University, Istanbul,34500, Turkey)

Received: 2015-08-07 Accepted : 2015-08-07 Published : 2009-04-01

Keywords: parabolic equations, Multipoint nonlocal boundary value problem, reverse type, difference equations, well-posedness, almost coercivity 2000 MSC: 47D06, 35K20,

Abstract :

We consider the Rothe difference scheme for approximate solution of the abstract parabolic equation in a Hilbert space with the nonlocal boundary condition. Theorems on stability estimates, coercivity and almost coercivity estimates for the solution of this difference scheme are established. In application, new coercivity inequalities for the solution of multi-point nonlocal boundary value difference equations of parabolic type are obtained.

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