A problem with nonlocal integral 1st kind conditions for 4th order partial differential equation

L. S. Pulkina

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 2, pp. 30-44

Résumé

In this article, we consider a nonlocal problem with integral conditions for one-dimensional 4th order partial differential equation. A distinguishing feature of this problem is the presence of integral conditions of the 1st kind. Moreover, the kernels of these conditions depend on both spatial and time variables. We suggest a new approach which enables to overcome the difficulties arising from the form of nonlocal conditions and derive a priori estimates. Obtained estimates play a significant role when we prove the existence and uniqueness of the solution to the problem.

Détail

Keywords: 4th-order partial differential equation, nonlocal problem, integral conditions of 1st and 2nd kind, generalized solution, Sobolev space, a priori estimates.

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