Electron. J. Differential Equations, Vol. 2017 (2017), No. 53, pp. 1-11.

Stability of boundary-value problems for third-order partial differential equations

Allaberen Ashyralyev, Kheireddine Belakroum, Assia Guezane-Lakoud

We consider a boundary-value problem for the third-order partial differential equation
 \frac{d^3u(t)}{dt^3}+Au(t)=f(t),\quad 0<t<1, \cr
 u(0)=\varphi,\quad u(1)=\psi,\quad u'(1)=\xi
in a Hilbert space H with a self-adjoint positive definite operator A. Using the operator approach, we establish stability estimates for the solution of the boundary value problem. We study three types of boundary value problems and obtain stability estimates for the solution of these problems.

Submitted December 14, 2016. Published February 21, 2017.
Math Subject Classifications: 35G15, 47A62.
Key Words: Stability; boundary value problem; Hilbert space; third order partial differential equation; self-adjoint positive definite operator.

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Allaberen Ashyralyev
Department of Mathematics
Near East University, Nicosia, TRNC
Mersin 10, Turkey
email: allaberen.ashyralyev@neu.edu.tr
Kheireddine Belakroum
Department of Mathematics
Frères Mentouri University
Constantine, Algeria
email: belakroumkheireddine@yahoo.com
Assia Guezane-Lakoud
Laboratory of Advanced Materials
Mathematics Department, Faculty of Sciences
Badji Mokhtar Annaba University
P.O. Box 12, Annaba, 23000, Algeria
email: a_guezane@yahoo.fr

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