A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations | Zendy

Allaberen Ashyralyev | Zendy

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A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations

Author(s) -

Allaberen Ashyralyev

Publication year - 2011

Publication title -

electronic journal of qualitative theory of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.524

H-Index - 33

ISSN - 1417-3875

DOI - 10.14232/ejqtde.2011.1.49

Subject(s) - mathematics , boundary value problem , mathematical analysis , parabolic partial differential equation , value (mathematics) , elliptic boundary value problem , mixed boundary condition , partial differential equation , statistics

The abstract nonlocal boundary value problem 8 − d 2 u(t) dt2 + sign(t)Au(t) = g(t),(0 t 1), du(t) dt + sign(t)Au(t) = f(t),(−1 t 0), u(1) = u(−1) + µ for the differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Holder spaces without a weight is established. The coercivity inequalities for solutions of the boundary value problem for elliptic-parabolic equations are obtained.

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