Electron. J. Differential Equations, Vol. 2019 (2019), No. 29, pp. 1-9.

Nonlocal approach to problems on longitudinal vibration in a short bar

Ludmila S. Pulkina, Alexander B. Beylin

In this article, we consider a problem with dynamic nonlocal conditions for a forth-order PDE with dominating mixed derivative. This problem is closely related to vibration problems, in particular, to longitudinal vibration in a short bar. The existence and uniqueness of a generalized solution are proved.

Submitted October 24, 2018. Published February 18, 2019.
Math Subject Classifications: 35L10, 35L20, 35L99.
Key Words: Nonlocal problem; longitudinal vibration; forth order equation; dynamical boundary condition; generalized solution.

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Ludmila S. Pulkina
Samara National Research University
Samara, Russia
email: louise@samdiff.ru
Alexander B. Beylin
Samara State Technical University
Samara, Russia
email: abeilin@mail.ru

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